Hybrid Hidden Markov Model for Modeling Equity Excess Growth Rate Dynamics: A Discrete-State Approach with Jump-Diffusion

Generating synthetic financial time series that preserve the statistical properties of real market data is essential for stress testing, risk model validation, and scenario design. Existing approaches struggle to simultaneously reproduce heavy-tailed distributions, negligible linear autocorrelation, and persistent volatility clustering. We developed a hybrid hidden Markov framework that discretized excess growth rates into Laplace quantile-defined states and augmented regime switching with a Poisson jump-duration mechanism to enforce realistic tail-state dwell times. Parameters were estimated by direct transition counting, bypassing the Baum-Welch EM algorithm and scaling to a 424-asset pipeline. Applied to ten years of daily equity data, the framework achieved high distributional pass rates both in-sample and out-of-sample while partially reproducing the volatility clustering that standard regime-switching models miss. No single model was best at everything: GARCH(1,1) better reproduced volatility clustering but failed distributional tests, while the standard HMM without jumps passed more distributional tests but could not generate volatility clustering. The proposed framework delivered the most balanced performance overall. For multi-asset generation, copula-based dependence models that preserved each asset's marginal HMM distribution substantially outperformed a Single-Index Model factor baseline on both per-asset distributional accuracy and correlation reproduction.