A contaminated generalized t model for cryptocurrency returns

Abstract

In financial analytics, a key aim of currency data analysis is to determine the distribution of returns. Considering the extensive utilization of cryptocurrencies, it is essential to offer a highly flexible model for distributions with heavier tails to analyze bitcoin data. A recent study by Punzo and Bagnato (2021) demonstrated that cryptocurrency returns have traits of high peakedness, heavy tails, and large excess kurtosis. To improve control over tail behaviour in flexible models, we recommend employing the generalized elliptical family of distributions for cryptocurrency returns.

We systematically construct this family of distributions, obtaining the Bernoulli-Laplace distribution from Punzo and Bagnato (2021) and the contaminated generalized t distribution as constituents of this family. Both distributions have heavy tails, pronounced peaks, and large adjustable kurtosis. Additionally, the suggested framework allows for the division of the real line into two regions: one containing typical points and the other containing atypical points.

We illustrate the effectiveness of the suggested framework utilizing four cryptocurrencies: USDJ USD, Frax USD, Gnosis USD, and Ethereum USD, in comparison to alternative distributions frequently employed in financial literature. The findings demonstrated that the suggested framework surpasses the other evaluated distributions. Moreover, the contaminated generalized t distribution is optimal for data with significant excess kurtosis, whereas the Bernoulli-Laplace distribution is preferable for data with comparatively lower kurtosis, while still leptokurtic.