Category: Finance & Banking Algorithms
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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.
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How Hidden-Markov Regime Algorithms Infer Financial States: Transition Matrices, Forward–Backward Filtering, Viterbi Paths, EM Calibration and Regime Failure
A mathematical guide to hidden-Markov financial regime inference: transition matrices, forward–backward filtering, Viterbi decoding, EM calibration, state duration, diagnostics and failure modes.
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How Risk-Parity Algorithms Solve Equal Risk Contributions: Euler Decomposition, Covariance Matrices, Nonlinear Solvers, Risk Budgets, Rebalancing and Failure Modes
A mathematical guide to risk parity and equal risk contribution: Euler decomposition, marginal contributions, covariance inputs, nonlinear solvers, risk budgets, leverage separation and failure diagnostics.
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How Ledoit–Wolf Covariance-Shrinkage Algorithms Stabilise Financial Risk Matrices: Bias–Variance Trade-Offs, Shrinkage Targets, Eigenvalues, Conditioning and Out-of-Sample Tests
A mathematical guide to Ledoit–Wolf covariance shrinkage: structured targets, shrinkage intensity, eigenvalue stabilisation, conditioning, inverse-covariance risk and out-of-sample diagnostics.
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How DCC-GARCH Algorithms Turn Volatility Shocks into Time-Varying Correlations: Two-Stage Estimation, Q-Matrix Recursion, Normalisation, Persistence and Failure Tests
A mathematical guide to DCC-GARCH: two-stage volatility and correlation estimation, Q-matrix recursion, normalisation, persistence, positive-definiteness, corrected DCC and failure diagnostics.
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How Carr–Madan FFT Option-Pricing Algorithms Turn Characteristic Functions into Strike Grids: Damping, Fourier Inversion, Aliasing, Quadrature and Convergence
A computational guide to Carr–Madan FFT option pricing: damping, characteristic functions, linked frequency/strike grids, quadrature, aliasing, truncation, interpolation and convergence tests.
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How Shapley-Value Risk-Allocation Algorithms Share Diversification Fairly: Coalitions, Marginal Contributions, Permutation Sampling, Euler Comparisons and Computational Limits
A mathematical guide to Shapley-value risk allocation: coalitions, marginal contributions, diversification sharing, permutation sampling, Euler comparisons and computational diagnostics.
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How Hawkes-Process Algorithms Model Self-Exciting Financial Events: Conditional Intensity, Branching Ratios, Multivariate Kernels, Calibration and False Causality
A mathematical guide to Hawkes processes in finance: conditional intensity, branching ratios, multivariate kernels, likelihood calibration, time-rescaling diagnostics and false-causality risks.