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

Ülkü Erisoglu; Selim Gunduz; Mert Yaman; Ülkü Erisoglu; Selim Gunduz; Mert Yaman

doi:10.3934/math.2026579

AIMS Mathematics

2026, Volume 11, Issue 5: 14096-14120. doi: 10.3934/math.2026579

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

1.
Department of Statistics, Faculty of Science, Necmettin Erbakan University Konya 42090, Turkey
2.
Department of Business Administration, Faculty of Economics, Administrative and Social Sciences, Adana Alparslan Türkeş Science and Technology University, Adana 01250, Turkey

Received: 19 March 2026 Revised: 26 April 2026 Accepted: 28 April 2026 Published: 19 May 2026
MSC : 62H10, 62P20

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.
- value-at-risk,
- backtest,
- cryptocurrencies,
- Monte Carlo simulation,
- Gaussian mixture model
Citation: Ülkü Erisoglu, Selim Gunduz, Mert Yaman. An enhanced Monte Carlo simulation framework with Backtest-Driven GMM and deterministic initialization for Portfolios risk estimation[J]. AIMS Mathematics, 2026, 11(5): 14096-14120. doi: 10.3934/math.2026579

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Abstract

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.

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