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 to modeling them properly. The Levy's stable distribution is one of the attractive distribution that well describes the fat tails and scaling phenomena in economic systems.In this paper, we show that the behaviors of price fluctuations in  cryptocurrency markets can also be characterized by a Levy's stable distribution  under certain conditions of time intervals ranging from 30 minutes to 4 hours. The arguments are developed under the theoretical background of the General Central Limit Theorem (GCLT) and quantitative valuation defined as a distance function using the Parseval's relation. Our approach can generally be extended for further analysis of statistical properties and  applications for financial modeling.
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 to modeling them properly. 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 fairly well by a Levy's stable distribution with alpha = 1.4, which indicates fatter tails compared to a Gaussian distribution. Moreover, we have come to realize the limitations of the stable model especially under certain conditions outside time intervals ranging from 30 minutes to 4 hours. The arguments are developed under the theoretical background of the General Central Limit Theorem (GCLT) and quantitative valuation defined as a distance function using the Parseval's relation. Our approach can generally be extended for further analysis of statistical properties and contribute to develop proper applications for financial modeling.
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