Modelling Extreme Tail Risk of Bitcoin Returns Using the Generalised Pareto Distribution

Abstract

This paper analyses the extreme tail behaviour of Bitcoin returns by fitting a Generalised Pareto Distribution (GPD). The GPD is used to model the extreme daily Bitcoin returns over the period 2008 to 2023. The returns above the chosen thresholds, for both Bitcoin gains and losses, are selected. The GPD is then fitted to the selected excess returns. The Anderson Darling (AD) and Kolmogorov Smirnov (K-S) goodness-of-fit tests reveal that the GPD captures the distribution of the Bitcoin excess returns. The Value at Risk (VaR) and Expected Shortfall (ES) under the GPD are used to measure the extreme tail risk of the Bitcoin returns. The upside risk (gains) is found to outweigh downside risk (losses), and this gives insight to investors interested in Bitcoin.