Characterizing Cryptocurrency market with Levy's stable distributions

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.

References in corpus (10)

• Power-law distributions in empirical data
• Scaling of the distribution of fluctuations of financial market indices
• Scaling properties of extreme price fluctuations in Bitcoin markets
• Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime
• Parameter estimation for stable distributions with application to commodity futures log returns
• Superposition of chaotic process with convergence to Levy's stable law
• A nonlinear population Monte Carlo scheme for the Bayesian estimation of parameters of $\alpha$-stable distributions
• Super Generalized Central Limit Theorem: Limit distributions for sums of non-identical random variables with power-laws
• Closed-form solutions for the Lévy-stable distribution
• GDP growth rates as confined Lévy flights

Cited by in corpus (2)

• Exploring asymmetric multifractal cross-correlations of price-volatility and asymmetric volatility dynamics in cryptocurrency markets
• Flexible Two-point Selection Approach for Characteristic Function-based Parameter Estimation of Stable Laws