Cryptocurrency risk management using Lévy processes and time-varying volatility

Abstract

This paper applies the Lévy-GJR-GARCH model to explore the empirical dynamics of Bitcoin, Ethereum, and Ripple. It highlights volatility clustering, pronounced skewness, and high kurtosis in cryptocurrency markets. The study finds that models integrating innovation distributions more accurately capture and explain the volatility processes and tail risks in these assets. Advanced models, especially those accounting for extreme tail-end and asymmetric jump effects, are better suited for adapting to market changes and providing precise risk indicators, effectively identifying potential losses.