Flexible probabilistic models for capturing extreme risk in Cryptocurrency returns
Applicable Nonlinear Analysis, Volume 4, Issue 1, April 2027, Pages: 10–28
Sayed Mohammed Zeeshan
Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh 202002 India
Feeroz Babu
Center of General Education, China Medical University, Taichung, 40447 Taiwan
Abstract
This study presents a comparative investigation of probabilistic mixture models for capturing extreme risk in cryptocurrency return distributions. Specifically, we evaluate the performance of the Gaussian Mixture Model (GMM), the Student-\(t\) Mixture Model (TMM), and the Laplace Mixture Model (LMM) using standardized daily return series from ten leading cryptocurrencies over five years. The primary objective is to assess each model's ability to accurately represent heavy tails and extreme return behavior, which are critical for reliable financial risk estimation. Model performance is evaluated using tail-sensitive risk measures, including Value-at-Risk (VaR) and Expected Shortfall (ES) at the 5% confidence level, alongside log-likelihood-based goodness-of-fit diagnostics. Empirical findings indicate that while the GMM effectively captures the central distribution, it systematically underestimates tail probabilities. The LMM provides moderate improvement in flexibility but does not consistently outperform alternative specifications in extreme regions. In contrast, the TMM demonstrates superior tail fit and delivers more accurate VaR and ES estimates across assets. These results underscore the importance of heavy-tailed mixture frameworks for robust risk modeling in high-volatility digital asset markets.
Cite this Article as
Sayed Mohammed Zeeshan and Feeroz Babu, Flexible probabilistic models for capturing extreme risk in Cryptocurrency returns, Applicable Nonlinear Analysis, 4(1), 10–28, 2027