Bayesian Forecasting of Value-at-Risk and Expected Shortfall in Cryptocurrency Markets: A Nonlinear Semi-Parametric Framework

Cryptocurrencies exhibit high volatility, emphasizing the importance of accurately measuring tail risk in their markets. This research incorporates a threshold-switching mechanism into Taylor's ES-CAViaR models that unveil features such as asymmetry and jump phenomena. These enhancements effectively capture the diverse tail risks of cryptocurrencies while enabling the simultaneous forecasting of both Value-at-Risk (VaR) and Expected Shortfall (ES). The proposed models incorporate two types of functions to address the VaR and ES nexus with the option to use the rolling standard deviation of returns as a short-term volatility proxy as a regressor. We estimate the parameters and forecast tail risk within a Bayesian framework. Taking the two largest cryptocurrencies by market capitalization, Bitcoin and Ethereum, we assess the one-step-ahead forecasting performance over a four-year out-of-sample period using a rolling window approach. The comparative results from backtests and five scoring functions among eight competing models support the conclusion that models with a threshold mechanism capture the tail risk of cryptocurrencies more accurately than other risk models.