[2603.10202] Hybrid Hidden Markov Model for Modeling Equity Excess Growth Rate Dynamics: A Discrete-State Approach with Jump-Diffusion

Quantitative Finance > Statistical Finance arXiv:2603.10202 (q-fin) [Submitted on 10 Mar 2026 (v1), last revised 2 Apr 2026 (this version, v2)] Title:Hybrid Hidden Markov Model for Modeling Equity Excess Growth Rate Dynamics: A Discrete-State Approach with Jump-Diffusion Authors:Abdulrahman Alswaidan, Jeffrey D. Varner View a PDF of the paper titled Hybrid Hidden Markov Model for Modeling Equity Excess Growth Rate Dynamics: A Discrete-State Approach with Jump-Diffusion, by Abdulrahman Alswaidan and Jeffrey D. Varner View PDF HTML (experimental) Abstract: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 ...