Category: Uncategorized
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How CCP Default-Waterfall Algorithms Allocate Clearing Losses: Margin, Defaulter Funds, Skin in the Game, Mutualised Default Funds, Assessments and Recovery Limits
How central counterparties sequence financial resources after a clearing-member default: defaulter margin and default-fund contributions, CCP capital, mutualised default funds, assessments, recovery tools and resolution boundaries—plus stress-sizing, incentive, contagion and model-risk diagnostics.
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How Dupire Local-Volatility Algorithms Extract Dynamics from Option Surfaces: Strike/Maturity Derivatives, Risk-Neutral Density, Numerical Smoothing and Model Failure
How Dupire’s local-volatility framework differentiates a smooth European option surface to recover an instantaneous volatility function, why density and calendar-arbitrage constraints matter, and how numerical noise, sparse strikes and wrong smile dynamics can make an apparently exact vanilla fit unreliable for exotics.
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How SVI Volatility-Surface Algorithms Fit Option Smiles: Total Variance, Log-Moneyness, Five Parameters, Static-Arbitrage Tests and Calibration Failure
How the Stochastic Volatility Inspired (SVI) parameterization turns noisy option quotes into smooth total-variance smiles, what its five raw parameters mean, how calendar and butterfly arbitrage are tested, and why a visually excellent fit can still be mathematically unusable.
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How FX-Forward Pricing Algorithms Turn Interest-Rate Curves into Forward Points: Covered Interest Parity, Discount Factors, Broken Dates, Cross-Currency Basis and No-Arbitrage Diagnostics
How foreign-exchange forward algorithms transform spot FX and two currency discount curves into outright forwards and swap points, handle broken dates and day counts, diagnose covered-interest-parity deviations, and separate no-arbitrage mathematics from cross-currency basis and market frictions.
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How Floating-Rate-Note Discount-Margin Algorithms Turn Reset Coupons into Market Value: Index Rates, Fixed Spreads, Forward Curves, Root Finding and Spread-Duration Diagnostics
How FRN valuation separates the reference index from the fixed quoted spread, projects future reset coupons, discounts the cash flows, and solves the extra discount margin that reconciles model cash flows to market price—plus Treasury FRN mechanics, reset risk, floors, accrued interest and spread-duration diagnostics.
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How Treasury STRIPS Algorithms Turn Coupon Bonds into Zero-Coupon Cash Flows: Stripping, Reconstitution, Discount Factors, No-Arbitrage Checks and Duration
How the U.S. Treasury STRIPS program separates each eligible note, bond or TIPS principal and interest payment into independently tradable zero-coupon components, how those components can be reconstituted, and how discount-factor replication, duration, liquidity and tax effects create verification tests and limits.
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How Black-76 and Bachelier Swaption Algorithms Price Rate Optionality: Forward Swap Rates, Annuities, Lognormal vs Normal Volatility and Negative-Rate Diagnostics
How payer and receiver swaptions reduce to option formulas on a forward swap rate multiplied by a swap annuity, why Black-76 uses lognormal percentage volatility while Bachelier uses absolute normal volatility, and how negative rates, shifts, smile calibration and parity tests expose model misuse.
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How Adjoint Algorithmic Differentiation Computes Derivatives Greeks at Scale: Computational Graphs, Reverse Accumulation, Bump-and-Revalue Benchmarks and Nondifferentiable Payoffs
How AAD turns a pricing program into a reverse computational graph so one valuation can produce sensitivities to thousands of risk factors at a small multiple of valuation cost—plus tape memory, Monte Carlo noise, discontinuous payoffs, regression boundaries and validation against bump-and-revalue.
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How Matched-Maturity FTP Algorithms Split Repricing Risk from Contingent Liquidity: Dual Horizons, Behavioural Deposits and Stress Consistency
A focused deep dive on matched-maturity FTP: split short repricing from long liquidity horizons, assign behavioural maturity to deposits, price contingent draws, and test stress-model consistency.