Modeling Cryptocurrency Returns with Alpha-Stable Distributions

Summary

This study evaluates alpha-stable distributions as models for returns of Bitcoin, Ethereum, and Ripple, which together represented most of the cryptocurrency market in the data considered. It focuses on whether this flexible heavy-tailed distribution can capture the leptokurtosis observed in crypto returns, a feature that simpler Gaussian models may miss.

The paper compares three parameter estimation approaches: maximum likelihood associated with DuMouchel, quantile-based estimation associated with McCulloch, and a sample-characteristics method associated with Koutrouvelis. It reports that maximum likelihood fits the examined return data better than the two alternatives and that the alpha-stable model captures their heavy tails. The distribution uses four free parameters, which the authors describe as parsimonious. The evidence is limited to the assets and sample examined; the abstract gives no dates, detailed fit statistics, forecasting tests, or evidence that the distribution improves portfolio decisions or trading performance.

Key ideas

• Alpha-stable distributions are assessed as models for heavy-tailed cryptocurrency returns.
• The empirical study examines Bitcoin, Ethereum, and Ripple returns.
• The authors report that maximum likelihood estimation fits the examined data better than quantile-based and sample-characteristics methods.
• The model captures the leptokurtic behavior reported in crypto returns.
• Goodness of fit alone does not establish improved forecasts or trading profitability.

Tags

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


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









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 $α$-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 $α$-stable distribution. The findings highlight that $α$-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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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