An Alpha-Stable Approach to Modelling Highly Speculative Assets and Cryptocurrencies

We investigate the behaviour of cryptocurrencies' return data. Using return data for bitcoin, ethereum and ripple which account for over 70% of the cyrptocurrency market, we demonstrate that α-stable distribution models highly speculative cryptocurrencies more robustly compared to 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 α-stable distribution. This papers covers predominant literature in cryptocurrencies and stable distributions.