Category: Finance & Banking Algorithms
-
How Expected-Shortfall Backtesting Algorithms Test Tail Severity: VaR–ES Joint Forecasts, Exceedance Residuals, Regression Tests and Small-Sample Failure
A mathematical guide to Expected Shortfall backtesting: VaR–ES joint calibration, exceedance residuals, regression tests, small-sample limits, diagnostics and falsification.
-
How Black–Litterman Portfolio Algorithms Blend Market Equilibrium with Views: Reverse Optimisation, Bayesian Updating, Confidence Matrices and Failure Diagnostics
A mathematical guide to Black–Litterman portfolio construction: reverse optimisation, equilibrium returns, Bayesian updating, view confidence, posterior returns, diagnostics and failure modes.
-
How Finite-Difference Option-Pricing Algorithms Solve the Black–Scholes PDE: Explicit, Implicit and Crank–Nicolson Grids, Stability, Boundary Conditions and Convergence
A computational guide to finite-difference option pricing: Black–Scholes PDE grids, explicit/implicit/Crank–Nicolson schemes, stability, boundaries, American exercise and convergence tests.
-
How Eisenberg–Noe Clearing Algorithms Propagate Interbank Defaults: Liability Matrices, Fixed Points, Fictitious Defaults, Uniqueness and Network Blind Spots
A mathematical guide to Eisenberg–Noe financial-network clearing: liability matrices, fixed-point payment vectors, default cascades, uniqueness, diagnostics, extensions and data blind spots.
-
How Extreme-Value Tail Algorithms Estimate Rare Financial Losses: Peaks Over Threshold, Generalized Pareto Tails, Threshold Diagnostics, VaR/ES and Model Failure
A mathematical guide to extreme-value tail estimation in finance: peaks over threshold, generalized Pareto fitting, tail quantiles, expected shortfall, threshold choice, diagnostics and failure modes.
-
How VaR Backtesting Algorithms Test Risk Forecasts: Exception Counts, Kupiec Coverage, Christoffersen Independence, Statistical Power and Failure Diagnostics
A mathematical guide to VaR backtesting: hit sequences, exception counts, Kupiec and Christoffersen tests, Basel diagnostics, statistical power, failure modes and verification.
-
How Survival-Analysis Algorithms Model When Loans Default: Cox Hazards, Censoring, Time-Varying Covariates, Competing Risks and Calibration Diagnostics
A mathematical guide to survival analysis for loan-default timing: hazard and survival functions, Cox models, censoring, time-varying covariates, competing risks, calibration, diagnostics and failure modes.
-
How Heath–Jarrow–Morton Algorithms Enforce No-Arbitrage Forward-Rate Dynamics: Volatility Surfaces, Drift Restriction, Factor Reduction, Simulation and Failure Tests
A mathematical guide to the Heath–Jarrow–Morton framework: forward-rate dynamics, the no-arbitrage drift restriction, factor reduction, discretisation, Monte Carlo checks, model limits and falsification tests.
-
How Hull–White Calibration Algorithms Fit Short-Rate Dynamics to Yield Curves and Swaption Prices: θ(t), Mean Reversion, Volatility, Repricing Tests and Identifiability
A mathematical guide to Hull–White one-factor calibration: fitting the initial curve, calibrating mean reversion and volatility, building trees, testing repricing, diagnosing identifiability and understanding model limits.