Continuous Hidden Markov Models for Equity Returns: Heavy-Tail Emission Families and Regime-Conditional Value-at-Risk

Battle Count: 72

Highly relevant for quantitative trading in several dimensions: (1) regime-conditional VaR provides interpretable tail-risk forecasts directly usable in risk management; (2) synthetic equity return generators support stress testing and backtesting of trading strategies; (3) multi-asset copula composition enables portfolio-level scenario generation; (4) explicit finite-state semantics allow regime interpretation for strategy timing; (5) the model reproduces key stylized facts (heavy tails, volatility clustering, negligible linear autocorrelation) essential for realistic simulation. However, the model is primarily a generative/analytical tool rather than a direct trading signal generator, and its performance degrades under regime introductions without periodic refit.

Moderate complexity. The core CHMM with Gaussian emissions uses standard Baum-Welch (well-known). Student-t and GED variants require ECM/ECME with numerical golden-section searches for shape parameters. Quantile-based initialization is straightforward. The spectral ACF identity requires eigendecomposition. Multi-asset copula composition adds rank-reordering simulation. The unified framework shares forward-backward recursions across all four families, reducing code duplication. Julia implementation with Flux.jl for QuantGAN baseline. Key challenges: numerical stability in log-space recursions, convergence of ECM block updates, and proper handling of nonconvex GED location objective.

Code available under MIT license at https://github.com/varnerlab/CHMM-Paper-Repository and https://github.com/varnerlab/CHMM-Model-Repository. Implemented in Julia. All seeds explicit, deterministic simulation protocol with 1,000 paths. Full algorithmic pseudocode provided in appendix. Vendor-stitch sanity check documented. Data sources specified (Polygon.io, Alpaca/IEX, CRSP).