An enhanced Monte Carlo simulation framework with Backtest-Driven GMM and deterministic initialization for Portfolios risk estimation

This study proposes an enhanced Gaussian mixture model (GMM)-based Monte Carlo simulation design to improve value-at-risk (VaR) estimation performance, specifically tailored for high-volatility environments such as global cryptocurrency markets. The proposed method deals with the critical problems of parameter instability due to random initialization and the limitations of determining the optimal number of components using standard information criteria like AIC or BIC, which are frequent challenges in traditional GMM-based VaR estimation approaches. To overcome these problems, a deterministic clustering algorithm was developed to ensure a stable initialization of GMM, and a simulation design like the parametric bootstrap was applied using the model fitted from observational data. Furthermore, a direct backtest performance was considered in determining the number of GMM components. The empirical application of the study was conducted through the VaR modeling of daily returns for a diversified portfolio consisting of BTC, ETH, BNB, and SOL crypto assets. A dynamic VaR model, utilizing 250-day rolling windows, was developed, and its performance was compared with traditional VaR estimation methods. VaR estimates, calculated at various confidence levels, consistently demonstrated that the proposed approach outperformed traditional methods. The results indicate that the proposed method markedly improves tail risk estimation accuracy, achieving higher success in satisfying both coverage and independence criteria.