Stock market simulator using hidden Markov generative model and its application in risk measurement

We propose a novel data-driven framework, called hidden Markov generative model, which combines the hidden Markov model (HMM) and a generative model for simulating a sequence of data. Specifically, we use the Wasserstein generative adversarial network (WGAN) as the generative model and use the resulting setup, HMM-WGAN, for simulating multivariate stock returns. In line with the original GAN model for images, we depict the invisible hands in financial markets as market painters and the different market regimes as distinct observable painting styles. The framework comprises of two phases. In Phase I, we train a time-homogeneous HMM to identify market painters for each trading day using a set of realized exogenous features. In Phase II, the painting style for each market painter is learned adversarially from a set of realized stock returns using WGAN. Subsequently, the market painter for the next trading day is simulated with the current regime and the trained HMM's transition matrix, and the consequent painting, i.e. multivariate stock returns, is then generated using the market painter's trained WGAN generator. Our empirical results demonstrate that the simulated multivariate stock returns not only replicate a comprehensive set of well-documented stylized facts—including heavy-tailed distributions, volatility clustering, and leverage effects—but also yield a more robust value-at-risk estimates compared to traditional approaches. As such, our framework provides a flexible, data-driven alternative to conventional parametric models without imposing restrictive assumptions.