Volatility estimation through stochastic processes: Evidence from cryptocurrencies

• A recently developed advanced stochastic volatility modeling is utilized for cryptocurrency volatility analysis. • The suggested Bayesian Markov Chain Monte Carlo (MCMC) sampling approach proves to be effective. • The modeling accurately captures the dynamics of stochastic volatility. • We incorporate the market risk method within the Basel IV regulations. We apply stochastic volatility modeling enriched with leverage and an asymmetrically heavy-tailed distribution to analyze the returns of Bitcoin and Ethereum. Our methodology leverages the generalized hyperbolic skew Student’s t-distribution (GH-ASV-skw-st) framework, as proposed by Nakajima and Omori (2012), employing a Bayesian Markov chain Monte Carlo (MCMC) sampling technique for effectiveness evaluation. The GH-ASV-skw-st model is demonstrated to adeptly capture the stochastic volatility patterns present in the returns of cryptocurrencies. After validation with several diagnostics and robustness checks, we illustrate the model’s suitability for high-volatility series by capturing asymmetry, leverage effects, and tail risk. Our findings indicate that the model fits the data more precisely than traditional models and provides a more reliable foundation for risk measures essential to portfolio management, such as Value at Risk (VaR) and Expected Shortfall (ES).