Cryptocurrency Volatility and Tail Risk

Abstract

Objective: This study aims to evaluate the performance of different ARMA-GARCH model specifications in the risk management of major cryptocurrencies, investigating whether the inclusion of exogenous variables improves the calibration of risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). Methodology: To achieve this objective, 4,032 specifications of the ARMA-GARCH model applied to the ten main cryptocurrencies in trading were tested. The study incorporated the Fear and Greed Index and Bitcoin Trading Volume as exogenous variables in an ARMA-GARCH-X framework, comparing the performance of the different specifications against an ARMA(1,1)-GARCH(1,1) benchmark. Originality: Despite growing interest in crypto asset risk management, there are still gaps in the literature regarding the effectiveness of incorporating exogenous variables into forecasting models, as well as the increase in the quality of forecasts when using more complex models. Main results: The results indicate that the inclusion of external variables improves risk calibration in some assets, although the gains are marginal and heterogeneous. There is also no single optimal parameterization, requiring ARMA orders, GARCH specifications, and error distributions to be adjusted for each cryptocurrency. Theoretical/methodological contributions: From a methodological point of view, the study contributes by demonstrating the importance of specific calibration of ARMA-GARCH models for different cryptocurrencies in risk estimation. Furthermore, the results suggest that, although more complex models can improve tail risk estimation, the gains in predictive power over simpler models are limited. Keywords: Cryptocurrencies; Risk Management; ARMA-GARCH; Value-at-Risk; Expected Shortfall.