This paper develops a Bayesian framework for modeling extreme downside risk in cryp-tocurrency markets, focusing on Bitcoin daily returns from 2014 to 2025. While the peaks-over-threshold (POT) approach from Extreme Value Theory (EVT) is widely used in risk management, its application in digital assets remains largely frequentist, offering limited insights into parameter uncertainty. By embedding the Generalized Pareto Distri-bution (GPD) within a Bayesian inferential structure, we estimate posterior distributions for the tail parameters and propagate them into Value-at-Risk (VaR) and Expected Short-fall (ES). The results confirm significantly heavy-tailed loss distributions, with a shape parameter around with a shape parameter around 0.21 (95% CI: 0.11–0.33). Posterior pre-dictive estimates indicate that Bitcoin’s daily 99% VaR is approximately −13.6%, while ES reaches −22.1%, underscoring the inadequacy of VaR as a sole risk measure. Importantly, posterior credible intervals highlight the uncertainty surrounding these estimates, offering risk managers probabilistic rather than deterministic assessments of tail risk. The findings not only provide empirical support for the regulatory shift from VaR to ES but also demonstrate the robustness of Bayesian EVT across prior choices. This study contributes to the literature by combining Bayesian inference with EVT in the context of cryptocurren-cy risk and offers a methodological foundation for future work on dynamic and mul-ti-asset tail modeling.
Bhat et al. (Thu,) studied this question.