Banking And Finance Mathematics | Market Risk, Value at Risk, Expected Shortfall and Stress Mathematics

Market-risk mathematics measures how changes in interest rates, credit spreads, foreign exchange, equities, commodities and volatility can change the value of a trading or investment portfolio. It ranges from local sensitivities such as delta, DV01 and vega to distributional measures such as Value at Risk (VaR), Expected Shortfall (ES), stress testing, backtesting, scenario analysis and liquidity-horizon adjustments.

For readers searching for market risk mathematics, VaR formula, Value at Risk, Expected Shortfall formula, CVaR, market risk Basel, FRTB, historical simulation VaR, parametric VaR, Monte Carlo VaR, backtesting VaR, stress testing, liquidity horizon, trading book risk, delta normal VaR or risk factor mapping, the central idea is that a portfolio loss is a function of market-factor moves. Risk measurement chooses a distribution/scenario for those moves and a valuation model that maps them into P&L.

The current Basel market-risk framework uses Expected Shortfall rather than VaR as the central tail metric for internal-model capital. The framework requires daily ES calculation, a 97.5% one-tailed confidence level and liquidity-horizon treatment built from a 10-day base horizon. That regulatory architecture is more detailed than any classroom formula, but the mathematical foundation is the same: define the loss distribution, model tail severity, account for nonlinear positions and verify forecasts through backtesting and stress. This article is educational, not regulatory or trading advice.

50-Second Router

• P&L function: maps market risk factors into portfolio profit/loss.
• Delta/DV01/vega: local first-order sensitivities; fast but incomplete for large moves.
• VaR: loss threshold exceeded only with a chosen tail probability under model assumptions.
• Expected Shortfall: average tail loss beyond the chosen VaR quantile under standard definitions.
• Historical simulation: replay historical factor changes through today’s portfolio.
• Parametric VaR: assume a statistical distribution/covariance structure.
• Monte Carlo: simulate factor scenarios from a model and full-revalue.
• Backtesting: compare predicted tail frequency/P&L with realised outcomes.
• Stress testing: revalue under severe coherent shocks outside ordinary statistical range.
• Liquidity horizon: risk must reflect time required to exit/hedge positions, not just one-day volatility.
• Non-modellable risk: sparse market data can require separate conservative treatment in regulatory frameworks.
• Verification: reconcile risk numbers to sensitivities, full repricing and actual P&L.

The Central Proposition: Risk Is a Distribution of Revalued Portfolios

Take today’s portfolio and market state. Move rates, spreads, FX, equity prices and volatilities according to many possible scenarios. Revalue the portfolio in each scenario. The resulting set of P&Ls is the market-risk distribution.

Everything else is a summary or decomposition. Delta says how value changes locally with one underlying. VaR chooses a quantile from the loss distribution. ES averages the tail. Stress testing selects deliberately severe scenarios. Backtesting compares model forecasts with realised P&L.

Adrian’s rule is to separate the scenario generator from the valuation engine. A good distribution with a bad pricing model is wrong; a perfect pricing model with unrealistic market scenarios is also wrong.

1. Market risk

Market risk is risk of loss from adverse market-price movements. It applies to rates, spreads, FX, equities, commodities and volatility. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Loss=L(Δrisk factors). For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Calling every investment loss market risk can blur credit/liquidity effects. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into trading risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

2. Risk factor

Risk factor is market variable driving value. It is the coordinate of the risk model. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Examples: 2y rate, USD/SGD, equity index, credit spread, implied vol. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Too few factors hide basis/curve/skew risk. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into factor mapping. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

3. P&L

P&L is change in portfolio value plus relevant cash flows over horizon. It is the object risk models distribute. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. P&L=V_t−V_0+cash flows. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Accounting P&L and hypothetical risk P&L can differ by framework. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk measurement. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

4. Loss variable

Loss variable is negative of P&L under a common convention. It lets larger numbers mean worse outcomes. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. L=−P&L. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Sign inconsistency can invert VaR/ES. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk metrics. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

5. Full revaluation

Full revaluation is repricing every position under each scenario. It captures nonlinearities directly. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. V_s=PricingModel(market_s). For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Computational cost can be high. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into Monte Carlo. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

6. Sensitivity approximation

Sensitivity approximation is using Greeks/DV01 to approximate P&L. It is faster than full revaluation. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. ΔV≈ΣSens_iΔx_i+second-order terms. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Large shocks make linear approximation inaccurate. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk engines. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

7. Delta

Delta is first derivative to underlying price. It captures local linear directional risk. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Δ=∂V/∂S. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Options change delta as market moves. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into equity/FX risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

8. Gamma

Gamma is second derivative to underlying. It captures curvature. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Γ=∂²V/∂S². For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Delta-neutral does not mean gamma-neutral. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into option risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

9. Vega

Vega is sensitivity to implied volatility. It captures volatility risk. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Vega=∂V/∂σ. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. One vega cannot describe skew/term-surface shifts. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into options. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

10. DV01

DV01 is currency value change for 1bp rate move. It is key rate-risk metric. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. DV01≈−∂V/∂y×0.0001. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Total DV01 hides curve shape. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into rates. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

11. CS01

CS01 is currency change for 1bp credit-spread move. It isolates spread risk. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. CS01≈−∂V/∂s×0.0001. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Credit spread and default risk are related but distinct. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into credit market risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

12. Beta

Beta is sensitivity to broad market factor. It maps portfolio to common equity factor. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. β=Cov(R_i,R_m)/Var(R_m). For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Historical beta can change in stress. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into equity risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

13. Basis risk

Basis risk is risk from imperfect co-movement between related factors. It survives simple hedges. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Residual depends on factor spread. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Hedged notional can still carry basis. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into hedging. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

14. Curve risk

Curve risk is risk from nonparallel changes across maturities. It requires multiple rate/spread factors. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Key-rate vector captures nodes. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Parallel shock alone is incomplete. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into rates. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

15. Volatility-surface risk

Volatility-surface risk is risk from skew/term-structure changes. It affects options beyond one vol number. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. IV=σ(K,T). For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Flat-vol stress misses wing/term movement. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into options. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

16. Correlation risk

Correlation risk is risk from changing dependence among factors. It affects portfolios and multi-asset derivatives. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Σ changes over time. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Calm-period correlations can understate crisis co-movement. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into portfolio risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

17. VaR

VaR is loss quantile at chosen horizon/confidence. It answers threshold question. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. VaR_α=quantile_α(L). For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. It does not tell severity beyond the threshold. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into tail risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

18. Expected Shortfall

Expected Shortfall is average loss in tail beyond VaR under standard continuous definition. It captures tail severity. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. ES_α=E[L|L≥VaR_α]. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Tail estimation is statistically noisy. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into tail risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

19. CVaR

CVaR is common term often used synonymously with Expected Shortfall in continuous settings. It is coherent under standard definitions. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. CVaR≈ES. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Definitions can differ in discrete distributions. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk theory. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

20. Confidence level

Confidence level is tail probability cutoff. It changes VaR/ES severity. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. 99% VaR uses 1% exceedance tail. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Higher confidence has fewer observations and more estimation error. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk metrics. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

21. Holding period

Holding period is time horizon over which risk is measured. Longer horizons generally widen loss distribution. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Horizon scaling sometimes uses sqrt time under restrictive assumptions. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Square-root scaling can fail with autocorrelation/nonlinearity. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk metrics. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

22. Normal VaR

Normal VaR is parametric VaR assuming normal P&L/returns. It gives simple analytic formula. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. VaR≈μ_L+z_ασ_L. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Normal model understates skew/fat tails. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into parametric risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

23. Delta-normal VaR

Delta-normal VaR is linear sensitivities plus multivariate normal factor changes. It scales efficiently for large portfolios. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. σ_P²=w’Σw or sensitivity covariance. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Options/nonlinear products need extensions/full revaluation. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk engines. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

24. Delta-gamma VaR

Delta-gamma VaR is approximation including second-order curvature. It improves nonlinear risk. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. ΔV≈Δ’x+0.5x’Γx. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Distribution becomes non-normal; approximations can be unstable. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into options risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

25. Historical simulation

Historical simulation is replay historical market moves on current positions. It preserves observed joint moves without parametric normality. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Loss_s=−[V(market0+historical shock_s)−V0]. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. History may omit future regimes. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into VaR/ES. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

26. Filtered historical simulation

Filtered historical simulation is rescales historical shocks for changing volatility. It addresses heteroskedasticity. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Standardise shocks then rescale by current volatility. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Volatility model adds model risk. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk models. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

27. Monte Carlo simulation

Monte Carlo simulation is simulate market-factor paths from statistical/stochastic models. It can handle nonlinear portfolios and novel scenarios. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Generate x_s→full revalue. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Model assumptions dominate tails. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk engines. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

28. Variance-covariance matrix

Variance-covariance matrix is second-moment dependence structure. It drives parametric portfolio risk. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. σ_P²=s’Σs. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Linear covariance misses tail dependence. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into portfolio risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

29. Cholesky simulation

Cholesky simulation is generate correlated normals using matrix factorisation. It is standard Monte Carlo technique. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. x=Lz where LL’=Σ. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Requires positive semidefinite covariance. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into simulation. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

30. Copula dependence

Copula dependence is joint-distribution model separating marginals and dependence. It can capture tail relationships beyond correlation. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Joint CDF=C(F1,…,Fn). For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Calibration can be unstable in tails. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk modelling. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

31. Fat tails

Fat tails is more probability in extremes than normal distribution. They raise tail losses. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Student-t/EVT are possible models. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. One heavy-tail family may still miss asymmetry/regimes. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into tail risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

32. Skewness

Skewness is asymmetry of return/loss distribution. It affects VaR/ES differently on each side. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Third standardised moment. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Variance alone cannot detect skew. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into distribution. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

33. Kurtosis

Kurtosis is tail/shape fourth-moment measure. It signals extreme observations. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Excess kurtosis >0 vs normal. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Sample kurtosis is unstable. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into distribution. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

34. Extreme value theory

Extreme value theory is tail-focused statistical framework. It models rare extremes directly. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. POT/GPD common approach. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Threshold choice and regime stability are difficult. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into tail risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

35. POT

POT is peaks over threshold method. It models exceedances above high threshold. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Excesses approximated by GPD under conditions. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Too-low threshold biases; too-high gives little data. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into EVT. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

36. GPD

GPD is Generalised Pareto distribution for tail exceedances. It estimates tail quantiles/ES. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Shape ξ controls tail heaviness. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. ξ estimation is noisy. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into EVT. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

37. Scenario analysis

Scenario analysis is full revaluation under chosen factor moves. It gives interpretable risk. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Scenario={rate,FX,equity,spread,vol changes}. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Scenario severity not probability unless explicitly modelled. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into stress. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

38. Stress testing

Stress testing is severe scenario analysis. It addresses distributional blind spots. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Stress loss=V_stress−V0. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. A stress set can still miss unknown unknowns. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk management. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

39. Historical stress

Historical stress is replay past crisis moves. It preserves a real joint event. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Use 2008,2020-style windows as relevant examples. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Future market structure can differ. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into stress. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

40. Hypothetical stress

Hypothetical stress is designed adverse scenario not seen historically. It targets current vulnerabilities. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Shock factors coherently. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Arbitrary shocks without narrative are weak. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into stress. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

41. Reverse stress

Reverse stress is find market moves causing a defined loss/limit breach. It identifies fragility. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Solve L(x)≥threshold. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. It finds pathways, not likelihood. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into stress. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

42. Backtesting

Backtesting is compare risk forecasts with realised/hypothetical P&L. It tests model calibration. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Count VaR exceptions and analyse residuals. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Good exception count can hide tail-severity/model issues. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into validation. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

43. VaR exception

VaR exception is loss exceeding predicted VaR. It is basic backtest event. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. I(L_t>VaR_t). For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Exception clustering matters. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into backtesting. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

44. Kupiec test

Kupiec test is unconditional coverage test for exception frequency. It checks observed exceedance rate. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Likelihood ratio vs nominal exceedance probability. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Does not test independence. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into backtesting. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

45. Christoffersen test

Christoffersen test is exception-independence/conditional coverage approach. It checks clustering. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Transition probabilities of exception state. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Small samples can have low power. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into backtesting. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

46. PIT test

PIT test is probability integral transform test for full predictive distribution. It goes beyond one quantile. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. u_t=F_t(realised). For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Conditional independence matters. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into distribution validation. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

47. Hypothetical P&L

Hypothetical P&L is P&L holding positions fixed while applying actual market moves. It isolates model risk factor mapping. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Used in certain regulatory backtests. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Excludes intraday/new-trade effects. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into market risk governance. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

48. Actual P&L

Actual P&L is real desk P&L including trading and other effects. It reflects business reality. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Includes new trades/fees/intraday effects. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Not directly comparable to risk model without decomposition. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into P&L explain. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

49. Risk-theoretical P&L

Risk-theoretical P&L is P&L generated using risk model factors only under regulatory framework. It tests whether risk factors explain desk P&L. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. RTPL vs HPL comparison in FRTB contexts. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Missing factors can fail attribution. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into FRTB. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

50. P&L attribution

P&L attribution is decompose realised P&L into modelled factor contributions. It tests sensitivity model completeness. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. P&L≈ΣSensitivity×Move+residual. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Large residual signals omitted/nonlinear factors. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into validation. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

51. Liquidity horizon

Liquidity horizon is time needed to exit/hedge risk under stressed markets. It scales risk beyond one-day assumption. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Basel ES uses prescribed liquidity horizons from 10-day base. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Actual liquidation may be longer in crisis. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into FRTB. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

52. 10-day base horizon

10-day base horizon is base horizon used in Basel internal-model ES construction. It anchors liquidity scaling. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. ES_T base at 10 days. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. It is regulatory convention, not universal economic truth. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into FRTB. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

53. 97.5% ES

97.5% ES is Basel IMA tail confidence level for ES. It replaces older 99% VaR capital core. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. One-tailed 97.5% ES. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Do not compare directly with 99% VaR without understanding definitions. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into FRTB. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

54. Risk-factor liquidity bucket

Risk-factor liquidity bucket is assignment of factor to prescribed liquidity horizon. It reflects market depth. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Longer horizon→larger scaled ES contribution. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Bucket assignment follows regulation. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into FRTB. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

55. Modellable risk factor

Modellable risk factor is factor with sufficient real-price observations under regulatory criteria. It can enter ES model. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Eligibility requires data frequency/quality tests. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Internal model use alone does not make factor modellable. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into FRTB. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

56. Non-modellable risk factor

Non-modellable risk factor is risk factor lacking sufficient observations. It receives separate stress capital treatment. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. NMRF charge based on stress scenario framework. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Sparse data creates conservatism. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into FRTB. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

57. Stressed ES

Stressed ES is ES calibrated/scaled using stress-period data under regulatory framework. It captures crisis conditions. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Calibration period selection matters. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. One historic stress may not match future vulnerabilities. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into FRTB. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

58. Trading desk

Trading desk is organisational unit for market-risk model approval/monitoring. FRTB applies model tests at desk level. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Desk eligibility depends on backtesting/P&L attribution. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Portfolio aggregation can hide weak desk models. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into governance. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

59. Standardised approach

Standardised approach is prescribed sensitivities/default/residual risk capital framework. It provides non-model capital and floor/backstop. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Sensitivities-based method under FRTB. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Not same as simple VaR. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into regulatory capital. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

60. Internal models approach

Internal models approach is approved ES-based method for eligible trading desks. It is subject to modellability and validation. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Capital includes ES,NMRF,default components. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Model approval is conditional. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into FRTB. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

61. Default risk charge

Default risk charge is capital for jump-to-default in trading book. It separates default tail from spread ES. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. DRC model/SA treatment applies. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Spread risk is not full default risk. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into FRTB. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

62. Residual risk add-on

Residual risk add-on is standardised add-on for exotic/nonlinear risks insufficiently captured. It recognises complex payoffs. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. RRAO under SA. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Not all option risk is captured by delta/vega/curvature alone. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into FRTB. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

63. Sensitivity-based method

Sensitivity-based method is FRTB SA method applying delta/vega/curvature sensitivities to prescribed shocks/correlations. It standardises capital. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Capital aggregated by buckets/risk classes. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Regulatory correlations are not empirical forecasts. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into FRTB. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

64. Curvature risk

Curvature risk is nonlinear loss beyond delta under prescribed shocks. It captures option convexity. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Curvature charge from up/down shocks. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Gamma alone may not match prescribed framework. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into FRTB. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

65. FX risk

FX risk is loss from currency moves. It can be linear or optional. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Position×FX shock plus option effects. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Translation and transaction exposure differ. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into market risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

66. Interest-rate risk

Interest-rate risk is loss from rate/curve changes in trading book. It spans tenor and basis factors. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Key-rate DV01/vega. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Banking-book IRRBB is a separate framework. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into market risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

67. Credit-spread risk

Credit-spread risk is mark-to-market loss from spread changes. It precedes default. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. CS01/curve sensitivities. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Spread and default can interact. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into market risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

68. Equity risk

Equity risk is loss from equity prices/volatility/dividends. It includes spot and options. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Delta/gamma/vega. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Index vs single-name basis matters. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into market risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

69. Commodity risk

Commodity risk is loss from commodity spot/forward curve moves. It includes location/grade/term basis. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Futures curve factors. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Physical constraints matter. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into market risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

70. Volatility risk

Volatility risk is loss from implied-vol changes. It is central to options. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Vega/surface factors. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Historical volatility alone is insufficient. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into market risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

71. Correlation risk

Correlation risk is loss from dependence shifts in multi-asset/structured products. It can be nonlinear. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Correlation Greeks or scenario revaluation. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Correlation spikes in stress. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into market risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

72. Gap risk

Gap risk is loss from discontinuous jumps. It evades continuous hedging. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Jump scenario/full revaluation. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. VaR based on smooth returns can understate. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into options. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

73. Event risk

Event risk is loss around discrete announcements/defaults. It is concentrated in time. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Scenario/event distribution. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Normal daily scaling is weak. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into market risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

74. Concentration risk

Concentration risk is large exposure to one factor/name. It increases tail vulnerability. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Position share or stress contribution. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Diversified VaR can hide name concentration. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk limits. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

75. Position limit

Position limit is maximum notional or risk exposure. It constrains size. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Limit by notional/sensitivity. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Notional alone can misstate option risk. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk management. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

76. Sensitivity limit

Sensitivity limit is cap on delta/DV01/vega etc. It controls local factor risk. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Compare current sensitivity with limit. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Can be gamed by nonlinear exposures. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk limits. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

77. VaR limit

VaR limit is cap on modelled quantile loss. It controls aggregate statistical risk. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Current VaR≤limit. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Model changes can alter limit usage. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk management. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

78. Stress-loss limit

Stress-loss limit is cap on severe-scenario loss. It protects against VaR blind spots. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. StressLoss≤limit. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Scenario set must remain relevant. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk limits. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

79. Stop-loss

Stop-loss is limit on realised P&L drawdown. It is outcome-based control. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Loss threshold triggers review/action. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. It can force trading at worst time. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk management. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

80. Hedge effectiveness

Hedge effectiveness is degree hedge reduces chosen risk. It should be measured by factor/P&L. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Residual variance/stress loss. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Hedge can lower VaR but raise liquidity risk. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk management. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

81. Margin liquidity

Margin liquidity is cash needed for collateral/variation margin. It converts market loss/volatility into funding need. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Margin calls follow MTM/IM models. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Market-risk hedge can still cause liquidity stress. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into cross-risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

82. Wrong-way risk

Wrong-way risk is exposure increases as counterparty quality worsens. It connects market and credit risk. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Joint scenarios exposure+PD. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Separate models can understate. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into CCR. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

83. Model risk

Model risk is loss/decision error from flawed valuation/risk model. It is material in nonlinear books. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Challenger models/full repricing. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Calibration fit is not proof. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into governance. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

84. Data quality

Data quality is accuracy/timeliness of prices and risk factors. It directly affects risk numbers. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Stale prices distort volatility/correlation. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. More history is not better if regimes/instruments changed. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into governance. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

85. Missing risk factor

Missing risk factor is economic driver omitted from model. It produces P&L residuals. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Detected via attribution/challenger tests. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Mapping proxy can fail under stress. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into validation. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

86. Proxy risk factor

Proxy risk factor is substitute series used when direct data unavailable. It introduces basis/model risk. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Proxy relationship estimated historically. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Crisis can break proxy link. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into risk modelling. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

87. Scenario library

Scenario library is governed set of historical/hypothetical stresses. It provides repeatable risk diagnostics. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Maintain versions and rationale. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Stale library misses new vulnerabilities. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into stress. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

88. Limit aggregation

Limit aggregation is combining risk across desks/factors. It needs consistent diversification assumptions. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Group risk ≠ simple sum if correlations recognised. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Excess diversification hides concentrations. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into enterprise risk. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

89. Capital allocation

Capital allocation is assigning market-risk capital to desks/products. It creates incentives/pricing signals. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Euler/marginal methods possible. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Allocation method can affect behaviour. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into management. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

90. RAROC market book

RAROC market book is profit relative to risk/economic capital. It evaluates risk-adjusted trading performance. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. RAROC=Risk-adjusted profit/Capital. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Short samples can reward hidden tail risk. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into performance. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

91. Risk-adjusted P&L

Risk-adjusted P&L is earnings after accounting for risk/capital cost. It discourages leverage-only profit. Market-risk mathematics must keep the loss horizon, factor set and valuation method attached to every number.

Mathematics. Profit−capital charge/expected losses. For local approximations state sensitivity units; for distributional metrics state horizon, confidence level, data window and valuation method.

Failure mode. Model risk can make adjusted metric fragile. Jo’s diagnostic is to compare the risk number with full-revaluation stress and realised P&L. A model that cannot explain its misses needs repair.

Connection. This feeds directly into management. Ryan would change the distribution, factor mapping or revaluation method one at a time to locate model sensitivity.

Worked Example 1: Parametric VaR

Portfolio daily P&L is approximated normal with mean 0 and standard deviation S$2m. 99% one-tailed z≈2.326. VaR≈S$4.652m.

The statement means modelled loss exceeds S$4.652m on about 1% of days under assumptions. It is not a maximum possible loss.

If distribution is fat-tailed, this VaR can materially understate extremes.

Worked Example 2: Normal Expected Shortfall

For a zero-mean normal loss with σ=S$2m, ES at confidence α uses σ φ(zα)/(1−α). At 97.5%, z≈1.96 and φ≈0.05844, giving ES≈2×0.05844/0.025≈S$4.675m.

The corresponding 97.5% VaR is about S$3.92m, so ES is larger because it averages losses beyond the threshold.

Basel’s regulatory ES adds liquidity-horizon/stress-period structure beyond this classroom formula.

Worked Example 3: Historical Simulation

Take 500 historical daily factor changes and full-revalue today’s portfolio under each. Sort 500 losses. A 99% VaR is near the fifth-worst observation under a chosen quantile convention.

The method automatically preserves historical joint rate/FX/equity moves, but only those seen in the sample.

A calm five-year window can dramatically understate crisis risk.

Worked Example 4: Delta-Normal Portfolio

Two risk-factor dollar sensitivities are S$1m and S$0.5m per 1% move. Factor volatilities are 1% and 2%, correlation 0.3. P&L standard deviation follows s’Σs.

Compute standalone dollar vols: 10k and 10k. Portfolio variance=10k²+10k²+2×0.3×10k×10k=260m, so σ≈S$16,125.

Correlation creates interaction; simple sum S$20k overstates diversified local risk.

Worked Example 5: Option Nonlinearity

Delta-neutral option position has gamma −0.04 and underlying moves +10. Second-order P&L≈0.5×−0.04×100=−2 per unit, despite zero initial delta.

A linear VaR using delta only would report near-zero directional risk. Full revaluation or delta-gamma method captures curvature.

This is why nonlinear desks need richer risk engines.

Worked Example 6: VaR Backtest

A 99% daily VaR model should produce roughly 2.5 exceptions over 250 days on average under ideal independent calibration. Observing 12 exceptions is a warning that coverage may be poor.

But exception count alone is insufficient: clustered exceptions and P&L attribution also matter.

Backtesting is model diagnosis, not just pass/fail arithmetic.

Worked Example 7: Liquidity-Horizon Intuition

A liquid FX factor might plausibly be hedged quickly; an illiquid credit tranche may require much longer. If both are measured only on one-day volatility, the second appears deceptively easy to exit.

Basel addresses this using prescribed liquidity horizons and a 10-day base ES construction. Economic risk managers can also use bespoke liquidation horizons.

Time-to-exit is part of market risk.

Worked Example 8: Stress versus VaR

Portfolio 99% one-day VaR=S$5m. A historical crisis scenario produces S$35m loss because rates, equities, FX and vol move jointly far beyond ordinary quantile scale.

This does not mean VaR is ‘wrong’; it answers a different question. The portfolio needs both statistical ordinary-tail and severe-scenario controls.

Risk dashboards should preserve those distinctions.

Worked Example 9: Spread Shock

Corporate bond position S$100m, spread duration 4.5. Credit spreads widen 150bp. First-order loss≈100m×4.5×0.015=S$6.75m.

Full revaluation may differ due to convexity, curve moves and default probability changes.

CS01/sensitivity gives transparent approximation for stress attribution.

Worked Example 10: Hedge Liquidity

A futures hedge reduces equity price risk but market drops sharply, generating positive hedge P&L; if the institution is short futures instead, variation margin might flow in. An options hedge may require premium but no daily VM depending on structure, while cleared derivatives may require IM changes.

Market-risk reduction and funding-liquidity effects depend on instrument structure.

A complete hedge decision should include both economic P&L and collateral cash-flow paths.

VaR and Expected Shortfall Are Not Competing Forecasts

VaR identifies a quantile boundary. ES estimates the average beyond that boundary. VaR is easier to backtest directly because exceedances are observable binary events; ES contains more information about tail severity but is statistically harder to validate. Regulatory frameworks often use both ES for capital and VaR-related backtesting/validation structures.

No single number answers every market-risk question. Sensitivities explain where risk comes from. VaR/ES summarise a distribution. Stress tests explore extreme coherent moves. Liquidity metrics ask whether positions can be exited or margined through the loss.

Mira’s rule: a good risk number should be paired with the question it answers.

A Professional Market-Risk Workflow

1. Map every position to market risk factors.
2. Calculate local sensitivities and reconcile to full valuation.
3. Build clean historical/current factor data.
4. Choose parametric, historical or Monte Carlo distribution model.
5. Calculate VaR/ES by desk and aggregate portfolio.
6. Full-reprice nonlinear products where material.
7. Run historical and hypothetical stresses.
8. Backtest exception frequency and P&L attribution.
9. Measure liquidity horizons, margin and concentration.
10. Apply model/data governance and challenger models.
11. Set sensitivity, VaR/ES and stress-loss limits.
12. Investigate realised losses outside model predictions.

Common Failure Modes

1. VaR called maximum loss

It is a quantile threshold. The repair is to restate the horizon, distribution, factor map and valuation method, then compare with full-revaluation stress.

2. ES called worst-case loss

It is a tail average, not maximum. The repair is to restate the horizon, distribution, factor map and valuation method, then compare with full-revaluation stress.

3. Normality assumed by convenience

Fat tails/skew can dominate. The repair is to restate the horizon, distribution, factor map and valuation method, then compare with full-revaluation stress.

4. One-day risk square-root scaled mechanically

Autocorrelation/nonlinearity/liquidity can invalidate. The repair is to restate the horizon, distribution, factor map and valuation method, then compare with full-revaluation stress.

5. Delta-only VaR on options

Gamma/vega/skew matter. The repair is to restate the horizon, distribution, factor map and valuation method, then compare with full-revaluation stress.

6. Historical simulation treated as model-free

Window choice and current-position mapping are assumptions. The repair is to restate the horizon, distribution, factor map and valuation method, then compare with full-revaluation stress.

7. Backtest count only

Clustering and P&L attribution matter. The repair is to restate the horizon, distribution, factor map and valuation method, then compare with full-revaluation stress.

8. Risk factor proxies ignored

Basis can break in stress. The repair is to restate the horizon, distribution, factor map and valuation method, then compare with full-revaluation stress.

9. Liquidity horizon ignored

Illiquid positions cannot be hedged instantly. The repair is to restate the horizon, distribution, factor map and valuation method, then compare with full-revaluation stress.

10. Stress scenario assigned fake probability

Severity and probability are distinct. The repair is to restate the horizon, distribution, factor map and valuation method, then compare with full-revaluation stress.

11. Diversification held fixed in crisis

Correlations can increase. The repair is to restate the horizon, distribution, factor map and valuation method, then compare with full-revaluation stress.

12. Market risk separated from margin liquidity

Collateral calls can create funding stress. The repair is to restate the horizon, distribution, factor map and valuation method, then compare with full-revaluation stress.

Formula Map

Measure	Simplified formula	Meaning
VaR	quantile_α(L)	Loss threshold.
Expected Shortfall	E[L|L≥VaR_α]	Average tail loss in continuous/simple case.
Normal VaR	μ_L+z_ασ_L	Parametric Gaussian quantile.
Portfolio variance	s’Σs	Linear sensitivity covariance risk.
Delta-gamma P&L	Δ’x+0.5x’Γx	Second-order approximation.
CS01 loss	≈CS01×spread bp move	Credit-spread P&L approximation.

Authoritative Reference Map

• Basel Framework — current market-risk framework
• Basel Framework — standards navigator
• Bukit Timah Tutor — How Banks Measure Market Risk: VaR, Expected Shortfall, Backtesting and Stress
• Extreme-Value Tail Algorithms

Connected Banking And Finance Mathematics Route

• Complete Banking And Finance Mathematics System
• Probability, Distributions and Financial Risk
• Options, Black–Scholes and Greeks
• Bank Stress Testing Mathematics
• Finance & Banking Algorithms

Applied Case Study 1: Rates trading desk

Situation. Book contains swaps and government bonds. The task is to map positions into factor distributions and nonlinear valuation effects.

Method. Measure key-rate DV01, curve stress, VaR/ES and liquidity horizon. Adrian checks sensitivities, Jo validates scenario generator, Aisha full-revalues tails, and Ryan compares VaR/ES with stress and realised P&L.

Boundary. Parallel duration alone misses slope/basis. Mira then identifies the risk that statistical history or local Greeks cannot see.

Applied Case Study 2: Equity options desk

Situation. Book is delta-neutral but short gamma/vega. The task is to map positions into factor distributions and nonlinear valuation effects.

Method. Use full revaluation, vol-surface stress and jump scenarios. Adrian checks sensitivities, Jo validates scenario generator, Aisha full-revalues tails, and Ryan compares VaR/ES with stress and realised P&L.

Boundary. Low delta VaR can hide nonlinear tail loss. Mira then identifies the risk that statistical history or local Greeks cannot see.

Applied Case Study 3: Credit trading desk

Situation. Corporate bonds and CDS have spread/default exposures. The task is to map positions into factor distributions and nonlinear valuation effects.

Method. Separate CS01, jump-to-default and liquidity stress. Adrian checks sensitivities, Jo validates scenario generator, Aisha full-revalues tails, and Ryan compares VaR/ES with stress and realised P&L.

Boundary. Spread loss and default risk need consistent aggregation. Mira then identifies the risk that statistical history or local Greeks cannot see.

Applied Case Study 4: FX book

Situation. Positions span spot, forwards and options. The task is to map positions into factor distributions and nonlinear valuation effects.

Method. Map currency delta, forward/basis and vol smile. Adrian checks sensitivities, Jo validates scenario generator, Aisha full-revalues tails, and Ryan compares VaR/ES with stress and realised P&L.

Boundary. Net notional can hide offsetting gross settlement/margin flows. Mira then identifies the risk that statistical history or local Greeks cannot see.

Applied Case Study 5: Commodity book

Situation. Exposure spans grades and delivery locations. The task is to map positions into factor distributions and nonlinear valuation effects.

Method. Stress spot, forward curve and location basis. Adrian checks sensitivities, Jo validates scenario generator, Aisha full-revalues tails, and Ryan compares VaR/ES with stress and realised P&L.

Boundary. Cross-hedge correlations can break. Mira then identifies the risk that statistical history or local Greeks cannot see.

Applied Case Study 6: Historical simulation

Situation. Desk uses 500-day window. The task is to map positions into factor distributions and nonlinear valuation effects.

Method. Compare calm-window and crisis-window risk estimates. Adrian checks sensitivities, Jo validates scenario generator, Aisha full-revalues tails, and Ryan compares VaR/ES with stress and realised P&L.

Boundary. Window choice materially changes tails. Mira then identifies the risk that statistical history or local Greeks cannot see.

Applied Case Study 7: Monte Carlo options

Situation. Desk uses stochastic-vol model. The task is to map positions into factor distributions and nonlinear valuation effects.

Method. Compare simulated ES with full-revaluation historical stress. Adrian checks sensitivities, Jo validates scenario generator, Aisha full-revalues tails, and Ryan compares VaR/ES with stress and realised P&L.

Boundary. Model calibration does not remove jump risk. Mira then identifies the risk that statistical history or local Greeks cannot see.

Applied Case Study 8: VaR exceptions cluster

Situation. Five exceptions occur in two weeks. The task is to map positions into factor distributions and nonlinear valuation effects.

Method. Test independence and volatility-regime response. Adrian checks sensitivities, Jo validates scenario generator, Aisha full-revalues tails, and Ryan compares VaR/ES with stress and realised P&L.

Boundary. Correct annual count can still hide clustering. Mira then identifies the risk that statistical history or local Greeks cannot see.

Applied Case Study 9: Illiquid credit tranche

Situation. Daily mark moves little. The task is to map positions into factor distributions and nonlinear valuation effects.

Method. Apply longer liquidation horizon and stress bid-ask/haircut. Adrian checks sensitivities, Jo validates scenario generator, Aisha full-revalues tails, and Ryan compares VaR/ES with stress and realised P&L.

Boundary. Low observed volatility can reflect stale pricing. Mira then identifies the risk that statistical history or local Greeks cannot see.

Applied Case Study 10: Margin shock

Situation. Cleared derivatives require large IM/VM after volatility spike. The task is to map positions into factor distributions and nonlinear valuation effects.

Method. Combine market loss with liquidity cash calls. Adrian checks sensitivities, Jo validates scenario generator, Aisha full-revalues tails, and Ryan compares VaR/ES with stress and realised P&L.

Boundary. Risk capital and liquidity buffers interact. Mira then identifies the risk that statistical history or local Greeks cannot see.

Applied Case Study 11: Concentration

Situation. One equity name dominates desk risk. The task is to map positions into factor distributions and nonlinear valuation effects.

Method. Run single-name crash and gap scenarios. Adrian checks sensitivities, Jo validates scenario generator, Aisha full-revalues tails, and Ryan compares VaR/ES with stress and realised P&L.

Boundary. Diversified portfolio VaR can understate concentrated jump loss. Mira then identifies the risk that statistical history or local Greeks cannot see.

Applied Case Study 12: Model proxy failure

Situation. Missing local bond curve mapped to global proxy. The task is to map positions into factor distributions and nonlinear valuation effects.

Method. Stress proxy basis breakdown. Adrian checks sensitivities, Jo validates scenario generator, Aisha full-revalues tails, and Ryan compares VaR/ES with stress and realised P&L.

Boundary. Risk-factor mapping is itself a risk. Mira then identifies the risk that statistical history or local Greeks cannot see.

Final Principle

Market risk is not one number. It is a map from uncertain market moves to portfolio losses, viewed locally through sensitivities, statistically through VaR/ES and structurally through stress and liquidity.

VaR draws a threshold. Expected Shortfall measures the tail beyond it. Backtesting checks whether forecasts match realised behaviour. Stress testing explores coherent adverse worlds. Liquidity horizons acknowledge that risk cannot always be exited at yesterday’s speed.

The strongest framework uses all of them together and demands that risk numbers explain actual P&L rather than merely look mathematically sophisticated.

The next owner moves from trading-book market risk to the banking book: asset–liability management, duration gaps, repricing, NII/EVE and immunisation.

Deep Practice Lab 1: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 2: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 3: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 4: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 5: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 6: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 7: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 8: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 9: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 10: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 11: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 12: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 13: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 14: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 15: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 16: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 17: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 18: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 19: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 20: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 21: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 22: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 23: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 24: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 25: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 26: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 27: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 28: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 29: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 30: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 31: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 32: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 33: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 34: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 35: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 36: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 37: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 38: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 39: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 40: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 41: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 42: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 43: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 44: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 45: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 46: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 47: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 48: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 49: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 50: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 51: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 52: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 53: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 54: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 55: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 56: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 57: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 58: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 59: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 60: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 61: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 62: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 63: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 64: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 65: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 66: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 67: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 68: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 69: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 70: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 71: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 72: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 73: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 74: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 75: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 76: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 77: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 78: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 79: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 80: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 81: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 82: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 83: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 84: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 85: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 86: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 87: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 88: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 89: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 90: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 91: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 92: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 93: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 94: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 95: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 96: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 97: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 98: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 99: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 100: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 101: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 102: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 103: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 104: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 105: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 106: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 107: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 108: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 109: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 110: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 111: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 112: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 113: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 114: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 115: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 116: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 117: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 118: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 119: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 120: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 121: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 122: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 123: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 124: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 125: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 126: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 127: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 128: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 129: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 130: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 131: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 132: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 133: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 134: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 135: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 136: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 137: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 138: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 139: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 140: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 141: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 142: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 143: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 144: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 145: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 146: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 147: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 148: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 149: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 150: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 151: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 152: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 153: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 154: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 155: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 156: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 157: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 158: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 159: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 160: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 161: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 162: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 163: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 164: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 165: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 166: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 167: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 168: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 169: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 170: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 171: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 172: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 173: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 174: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 175: Add liquidity horizon

Take risk factors with different liquidation horizons and compare one-day versus horizon-adjusted risk. Explain why sqrt-time is only approximation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 176: Compare VaR methods

Use one portfolio and calculate normal VaR, historical simulation VaR and Monte Carlo VaR. Explain differences from distribution and valuation assumptions.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 177: Calculate ES from sample

Sort a simulated/historical loss series and average observations beyond chosen quantile. Compare ES sensitivity to a single extreme observation.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 178: Backtest a VaR model

Generate 500 daily forecasts/outcomes. Count exceptions, test clustering conceptually and analyse worst exceptions by factor.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.

Deep Practice Lab 179: Stress option nonlinearity

Compare delta-only, delta-gamma and full-revaluation losses under progressively larger spot/vol shocks.

Complete the lab with explicit horizon, confidence level, data window and valuation method. Ben should reconcile loss signs, Clara should document market data, and Ethan should identify which tail assumption changes the result most.

Then replace one model assumption—normal tails, constant correlation or linear valuation—and rerun. The goal is to see model risk as part of market risk rather than a separate footnote.