Category: Finance & Banking Algorithms
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How Maximum-Entropy Interbank Reconstruction Algorithms Infer Missing Bilateral Exposures: Row/Column Constraints, RAS Scaling, Structural Zeros, Sparsity Bias and Contagion Bounds
A mathematical guide to maximum-entropy interbank network reconstruction: exposure matrices, row/column margins, RAS/IPF scaling, structural zeros, sparse alternatives and contagion-model uncertainty.
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How Filtered Historical Simulation Algorithms Turn Old Returns into Current VaR and Expected Shortfall: Volatility Filtering, Residual Resampling, Revaluation, Backtesting and Regime Failure
A mathematical guide to filtered historical simulation: volatility filtering, standardized residuals, synchronized bootstrapping, multi-step revaluation, VaR/ES, backtesting and regime-failure diagnostics.
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How Merton Jump-Diffusion Algorithms Price Discontinuous Returns: Poisson Jumps, Drift Compensation, Black–Scholes Mixtures, Smile Calibration and Hedge Failure
A mathematical guide to Merton jump diffusion: Poisson jumps, drift compensation, lognormal jump sizes, Black–Scholes mixtures, smile calibration, simulation and hedge failure.
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How Continuous-Time Credit-Migration Algorithms Turn Rating Histories into Generator Matrices: Transition Intensities, Matrix Exponentials, Embeddability, Default Absorption and Markov Failure
A mathematical guide to continuous-time credit migration: generator matrices, transition intensities, matrix exponentials, embeddability, default absorption, duration estimation and Markov failure.
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How Importance-Sampling Algorithms Estimate Rare Financial Losses Efficiently: Change of Measure, Likelihood Ratios, Exponential Tilting, Weight Degeneracy and Validation
A mathematical guide to importance sampling for rare financial events: change of measure, likelihood ratios, exponential tilting, weight degeneracy, VaR/ES estimation and validation.
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How Vine-Copula Algorithms Build High-Dimensional Financial Dependence: Pair-Copula Trees, Tail Asymmetry, h-Functions, Structure Selection and Failure Diagnostics
A mathematical guide to vine-copula dependence: pair-copula trees, h-functions, structure and family selection, tail asymmetry, simulation, diagnostics and failure modes.
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How Probability-Integral-Transform Algorithms Test Full Financial Forecast Distributions: PIT Uniformity, Berkowitz Tests, Dependence, Tail Misses and Calibration Failure
A mathematical guide to full-distribution forecast testing in finance: probability integral transforms, PIT histograms, Berkowitz tests, dependence diagnostics, proper scores and calibration failure.
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How Particle-Filter Algorithms Track Stochastic Volatility: Sequential Bayesian Weights, ESS, Resampling, Likelihood Estimation, Degeneracy and Model Failure
A mathematical guide to particle filtering for stochastic volatility: sequential Bayes updates, particle weights, ESS, resampling, likelihood estimation, smoothing, degeneracy and failure diagnostics.
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How Sobol Quasi-Monte Carlo Algorithms Price Derivatives Faster: Low-Discrepancy Points, Scrambling, Brownian Bridges, Effective Dimension and Convergence Failure
A computational guide to Sobol quasi-Monte Carlo in finance: low discrepancy, scrambling, Brownian bridges, PCA, effective dimension, randomized error estimation and convergence failure.