Lévy processes on the cryptocurrency market

Damian Zięba ()
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Damian Zięba: Faculty of Economic Sciences, University of Warsaw

No 2019-15, Working Papers from Faculty of Economic Sciences, University of Warsaw

Abstract: Lévy processes are very often used in financial modelling since they address various characteristics of financial data. One of those characteristics is the heavy-tailedness of probability density functions - a very common empirical stylized fact on the cryptocurrency market. The aim of this study was to determine which type of Lévy motion fits the data of cryptocurrencies better, namely Alpha-Stable distribution or one of distributions from the family of generalized hyperbolic motions. The log-returns of 227 cryptocurrencies, standardized by the realized volatility estimated with the GARCH (1,1), were fitted to 11 types of distributions. The results show that the generalized hyperbolic motions fit the cryptocurrency data much more accurately than the Alpha-Stable distribution, similarly as in the case of TOP100 NASDAQ stocks. In the further stage of the analysis, it is shown how the distribution of cryptocurrency data varies over time, i.e. before, during, and after the ‘boom-period’ of 2017/2018.

Keywords: cryptocurrency market; distribution fitting; Generalized Hyperbolic distribution; Alpha-Stable distribution; Lévy process (search for similar items in EconPapers)
JEL-codes: C10 C30 G15 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2019
New Economics Papers: this item is included in nep-pay
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https://www.wne.uw.edu.pl/index.php/download_file/5027/ First version, 2019 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:war:wpaper:2019-15

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