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Lévy processes on the cryptocurrency market

Author

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  • Damian Zięba

    (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.

Suggested Citation

  • Damian Zięba, 2019. "Lévy processes on the cryptocurrency market," Working Papers 2019-15, Faculty of Economic Sciences, University of Warsaw.
    • Handle: RePEc:war:wpaper:2019-15
    as

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    File URL: https://www.wne.uw.edu.pl/index.php/download_file/5027/
    File Function: First version, 2019
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    cryptocurrency market; distribution fitting; Generalized Hyperbolic distribution; Alpha-Stable distribution; Lévy process;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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