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

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Highly relevant for quantitative trading through synthetic data generation for backtesting, stress testing, and scenario analysis. The framework enables Monte Carlo-based risk metrics (VaR, CVaR) at scale across 424 assets. Regime-switching structure provides interpretable market states (crash, bear, neutral, bull, rally) useful for strategy development. However, the model is primarily a generative/simulation tool rather than a direct trading signal generator. The computational efficiency (no EM algorithm) makes it practical for daily/weekly scenario regeneration. Multi-asset copula extension supports portfolio-level risk assessment.

Moderate complexity. The core HMM with quantile partitioning and direct transition counting is computationally trivial and initialization-free (no Baum-Welch EM). The jump-duration mechanism adds two hyperparameters requiring grid search. Student-t emissions are straightforward. The main complexity lies in: (1) the multi-objective grid search over (epsilon, lambda) with 200 paths per grid point, (2) copula-based multi-asset extension with rank reordering, and (3) proper evaluation across multiple metrics. The Julia implementation (JumpHMM.jl) provides a ready-to-use package. Scaling to 424 assets is feasible due to the O(N^2) transition matrix counting approach.

Full code available under MIT license at https://github.com/varnerlab/HMM-w-jumps-paper.git. Core model logic implemented in Julia package JumpHMM.jl (https://github.com/varnerlab/JumpHMM.jl.git). Training and testing data included. Algorithms 1-4 fully specified. All hyperparameters, grid search ranges, and evaluation metrics documented. 424-asset pipeline described in detail.