A Theoretical Framework for Dynamic Volatility Analysis in Slot Machines: A Regime-Switching Hidden Markov Model (MS-HMM) Approach

This paper presents a theoretical framework that addresses the limitations of traditional, static volatility analysis in multi-state stochastic systems. By implementing a Regime-Switching Hidden Markov Model (MS-HMM) grounded in Extreme Value Theory (EVT), this approach accurately captures the volatility dynamics and conditional heteroskedasticity inherent in modern game design. The proposed analytical framework allows for the exact calculation of a robust, dynamic volatility index without relying on Monte Carlo simulations, outperforming standard Independent and Identically Distributed (IID) assumptions.