An $α$-Stable Approach to Modelling Highly Speculative Assets and Cryptocurrencies

Abstract: We investigate the behaviour of cryptocurrencies using data for bitcoin, ethereum and ripple which account for over 70% of the cryptocurrency market. We demonstrate that $\alpha$-stable distribution is an appropriately sufficient model for highly speculative cryptocurrencies which outperforms other heavy tailed distributions that are used in financial econometrics. We find that the maximum likelihood method proposed by DuMouchel (1971) produces estimates that fit the cryptocurrency return data much better than the quantile based approach of McCulloch (1986) and sample characteristic method by Koutrouvelis (1980). The empirical results show that the leptokurtic feature presented in cryptocurrency return data can be captured by an $\alpha$-stable distribution. The findings highlight that $\alpha$-stable distribution is not only parsimonious with its four free parameters but also a creative model that is close to reality. This paper covers early reports and literature on cryptocurrencies and stable distributions.