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Option Pricing With Heavy-Tailed Distributions Of Logarithmic Returns

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  • LASKO BASNARKOV

    (Faculty of Computer Science and Engineering, SS. Cyril and Methodius University, Skopje, Macedonia2Macedonian Academy of Sciences and Arts, Skopje, Macedonia)

  • VIKTOR STOJKOSKI

    (Macedonian Academy of Sciences and Arts, Skopje, Macedonia)

  • ZORAN UTKOVSKI

    (Fraunhofer Heinrich Hertz Institute, Berlin, Germany)

  • LJUPCO KOCAREV

    (Faculty of Computer Science and Engineering, SS. Cyril and Methodius University, Skopje, Macedonia2Macedonian Academy of Sciences and Arts, Skopje, Macedonia)

Abstract

A growing body of literature suggests that heavy tailed distributions represent an adequate model for the observations of log returns of stocks. Motivated by these findings, here, we develop a discrete time framework for pricing of European options. Probability density functions of log returns for different periods are conveniently taken to be convolutions of the Student’s t-distribution with three degrees of freedom. The supports of these distributions are truncated in order to obtain finite values for the options. Within this framework, options with different strikes and maturities for one stock rely on a single parameter — the standard deviation of the Student’s t-distribution for unit period. We provide a study which shows that the distribution support width has weak influence on the option prices for certain range of values of the width. It is furthermore shown that such family of truncated distributions approximately satisfies the no-arbitrage principle and the put-call parity. The relevance of the pricing procedure is empirically verified by obtaining remarkably good match of the numerically computed values by our scheme to real market data.

Suggested Citation

  • Lasko Basnarkov & Viktor Stojkoski & Zoran Utkovski & Ljupco Kocarev, 2019. "Option Pricing With Heavy-Tailed Distributions Of Logarithmic Returns," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 1-35, November.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:07:n:s0219024919500419
    DOI: 10.1142/S0219024919500419
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    Cited by:

    1. Viktor Stojkoski & Trifce Sandev & Lasko Basnarkov & Ljupco Kocarev & Ralf Metzler, 2020. "Generalised geometric Brownian motion: Theory and applications to option pricing," Papers 2011.00312, arXiv.org.

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