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

Paper: arXiv 2603.10202

Authors: Abdulrahman Alswaidan, Jeffrey D. Varner

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 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.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 8.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a pragmatic hybrid Hidden Markov Model combining Laplace quantile state discretization and a Poisson jump-duration mechanism to overcome the traditional volatility clustering limitations of standard HMMs. It demonstrates high empirical rigor through a large-scale evaluation over a 424-asset dataset across multiple metrics (KS, AD, Wasserstein, Hellinger, ACF-MAE) and copula-based multi-asset dependencies.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Generate synthetic equity data matching heavy tails, low autocorrelation, and volatility clustering"] --> B["Input Data:<br>10 years of daily equity data (424 assets)"]
    
    subgraph Methodology & Computation
        B --> C["Discretize Excess Growth:<br>Laplace quantile-defined states"]
        C --> D["Parameter Estimation:<br>Direct transition counting (bypassing Baum-Welch)"]
        D --> E["Hybrid Model Construction:<br>Discrete-state HMM + Poisson jump-duration mechanism"]
        E --> F["Multi-Asset Extension:<br>Copula-based dependence modeling vs. SIM baseline"]
    end

    F --> G["Key Outcomes & Findings:<br>1. Highest overall balance of distributional accuracy & volatility clustering<br>2. Outperformed standard HMM (no clustering) & GARCH(1,1) (failed distributions)<br>3. Copula extension preserved marginals & correlation better than SIM"]

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0 of 89 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.