Characterizing Cryptocurrency market with Levy's stable distributions

TL;DR

This paper demonstrates that cryptocurrency price fluctuations can be effectively modeled using Levy's stable distributions, capturing their fat tails and scaling behaviors across various time intervals.

Contribution

It introduces a quantitative method to characterize cryptocurrency market fluctuations with Levy's stable distributions, supported by likelihood ratio comparisons.

Findings

Cryptocurrency returns follow Levy's stable distribution with alpha around 1.4.

The model fits well for time intervals from 30 minutes to 4 hours.

The approach enhances understanding of statistical properties in crypto markets.

Abstract

The recent emergence of cryptocurrencies such as Bitcoin and Ethereum has posed possible alternatives to global payments as well as financial assets around the globe, making investors and financial regulators aware of the importance of modeling them correctly. The Levy's stable distribution is one of the attractive distributions that well describes the fat tails and scaling phenomena in economic systems. In this paper, we show that the behaviors of price fluctuations in emerging cryptocurrency markets can be characterized by a non-Gaussian Levy's stable distribution with $\alpha \simeq 1.4$ under certain conditions on time intervals ranging roughly from 30 minutes to 4 hours. Our arguments are developed under quantitative valuation defined as a distance function using the Parseval's relation in addition to the theoretical background of the General Central Limit Theorem (GCLT). We also discuss the fit with the Levy's stable distribution compared to the fit with other distributions by employing the method based on likelihood ratios. Our approach can be extended for further analysis of statistical properties and contribute to developing proper applications for financial modeling.