The Statistics of Bitcoin and Cryptocurrencies

Abstract

Cryptocurrencies became popular with the emergence of Bitcoin and have shown an unprecedented growth over the last few years. As of November 2016, more than 720 cryptocurrencies exist, with Bitcoin still being the most popular one. We show the statistical properties of the most important cryptocurrencies. We characterize their exchange rates versus the US Dollar by fitting parametric distributions to them, including the Student t distribution, the generalized hyperbolic distribution as well as the asymmetric normal inverse Gaussian and the asymmetric variance gamma distribution. Our findings show that cryptocurrencies exhibit strong non-normal characteristics, with standard heavy-tailed distributions such as the Student t distribution giving good descriptions of the data. This is the first study that looks at the parametric distribution of cryptocurreny returns. The results are important for investment and risk management purposes.