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.
Highlights
Cryptocurrencies have attracted considerable attention across the world as a newly emerging financial asset
This paper has explored the behaviors of price fluctuations in cryptocurrency markets by applying the Lévy’s stable distribution and discussed its validity for the empirical analysis
We introduce a numerical approach based on the CF and a theoretical approach based on the General Central Limit Theorem (GCLT) to find evidence for stable laws, by focusing on the time scaling behavior with different time intervals
Summary
Cryptocurrencies have attracted considerable attention across the world as a newly emerging financial asset. In a theoretical context, Lévy’s stable distribution is closely related to an essential theorem — the Generalized Central Limit Theorem (GCLT)13) that thoroughly explains the scaling phenomena in financial markets. We analyze the price fluctuation behaviors of emerging cryptocurrency markets with the Lévy’s stable distribution and examine the validity of the model. The idea proposed in this paper is helpful to value the liquidity conditions of the market and provide clues towards financial modeling in a more careful manner
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