Category: Finance & Banking Algorithms
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How Girsanov Change-of-Measure Algorithms Turn Real-World Drifts into Risk-Neutral Pricing: Radon–Nikodym Weights, Market Price of Risk, Martingales and Failure Cases
A mathematical guide to Girsanov in finance: Radon–Nikodym density processes, market price of risk, Brownian drift changes, equivalent martingale measures, numeraires, incompleteness and failure diagnostics.
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How Variance-Gamma Algorithms Price Pure-Jump Returns: Gamma Time Change, Characteristic Functions, Martingale Correction, Exact Increments and Calibration Failure
A mathematical guide to Variance-Gamma finance algorithms: gamma time change, pure-jump returns, characteristic functions, martingale correction, exact increment simulation, calibration and falsification.
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How Andersen QE Algorithms Simulate Heston Stochastic Volatility: Moment Matching, Positive Variance, Two Regimes, Martingale Correction and Monte Carlo Failure Tests
A mathematical guide to Andersen’s Quadratic-Exponential Heston simulation: CIR moment matching, positive variance, two transition regimes, martingale correction, convergence and failure diagnostics.
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How Saddlepoint Algorithms Approximate Credit-Portfolio Tails: Cumulant Generating Functions, Exponential Tilting, Lugannani–Rice, Root Finding, Lattice Corrections and Failure Tests
A mathematical guide to saddlepoint credit-tail algorithms: cumulant generating functions, exponential tilting, Lugannani–Rice tails, root finding, lattice corrections and failure diagnostics.
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How Rough Bergomi Algorithms Model Non-Markovian Volatility: Fractional Kernels, Hurst Exponents, Forward Variance, Hybrid Simulation and Calibration Failure
A mathematical guide to rough Bergomi algorithms: fractional kernels, Hurst roughness, forward variance, hybrid Monte Carlo simulation, calibration, diagnostics and model failure.
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How Base-Correlation Algorithms Calibrate Credit-Index Tranches: Attachment/Detachment, Equity-Tranche Bootstraps, Gaussian Copulas, Correlation Skews and Arbitrage Diagnostics
A mathematical guide to base-correlation calibration for credit-index tranches: loss layers, equity-tranche bootstraps, Gaussian copulas, correlation skews, interpolation and arbitrage diagnostics.
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How Black–Cox First-Passage Algorithms Model Corporate Default Before Maturity: Asset Barriers, Hitting Times, Survival Curves, Calibration and Structural Failure
A mathematical guide to Black–Cox first-passage credit algorithms: asset barriers, hitting times, survival curves, calibration, simulation bias, falsifiers and structural model limits.
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How Cox–Ingersoll–Ross Short-Rate Algorithms Keep Interest Rates Nonnegative: Square-Root Diffusion, Feller Boundary, Exact Simulation, Bond Prices, Calibration and Model Failure
A mathematical guide to the Cox–Ingersoll–Ross short-rate model: square-root diffusion, Feller boundary, exact noncentral-chi-square simulation, affine bond pricing, calibration and failure diagnostics.
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How Fourier-COS Option-Pricing Algorithms Turn Characteristic Functions into Prices: Cosine Density Expansion, Payoff Coefficients, Truncation Ranges, Convergence and Greek Failure
A computational guide to Fourier-COS option pricing: cosine density expansion, characteristic-function coefficients, payoff integrals, truncation-range selection, convergence diagnostics and Greek failure modes.