Lévy processes in the cryptocurrency market

Abstract

The aim of this study was to determine which type of Lévy motion fits the data of cryptocurrencies better, namely Alpha-Stable distribution or one of distributions from the family of generalized hyperbolic motions. The log-returns of 227 cryptocurrencies, standardized by the realized volatility estimated with the GARCH (1,1), were fitted to 11 types of distributions. The results show that the generalized hyperbolic motions fit the cryptocurrency data much more accurately than the Alpha-Stable distribution, similarly as in the case of TOP100 NASDAQ stocks. In the further stage of the analysis, it is shown how the distribution of cryptocurrency data varies over time, i.e. before, during, and after the 'boom-period' of 2017/2018.