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Pricing European options with a log Student’s t-distribution: A Gosset formula

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  • Cassidy, Daniel T.
  • Hamp, Michael J.
  • Ouyed, Rachid

Abstract

The distributions of returns for stocks are not well described by a normal probability density function (pdf). Student’s t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of European call or put options using a log Student’s t-distribution, which we call a Gosset approach in honour of W.S. Gosset, the author behind the nom de plume Student. The approach that we present can be used to price European options using other distributions and yields the Black–Scholes formula for returns described by a normal pdf.

Suggested Citation

  • Cassidy, Daniel T. & Hamp, Michael J. & Ouyed, Rachid, 2010. "Pricing European options with a log Student’s t-distribution: A Gosset formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5736-5748.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:24:p:5736-5748
    DOI: 10.1016/j.physa.2010.08.037
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    3. Claudia Yeap & Simon S Kwok & S T Boris Choy, 2018. "A Flexible Generalized Hyperbolic Option Pricing Model and Its Special Cases," Journal of Financial Econometrics, Oxford University Press, vol. 16(3), pages 425-460.
    4. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    5. Federica De Domenico & Giacomo Livan & Guido Montagna & Oreste Nicrosini, 2023. "Modeling and Simulation of Financial Returns under Non-Gaussian Distributions," Papers 2302.02769, arXiv.org.
    6. Wang, Xiao-Tian & Li, Zhe & Zhuang, Le, 2017. "European option pricing under the Student’s t noise with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 848-858.
    7. 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.
    8. Till Massing, 2019. "What is the best Lévy model for stock indices? A comparative study with a view to time consistency," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 33(3), pages 277-344, September.
    9. Rui Li & Saralees Nadarajah, 2020. "A review of Student’s t distribution and its generalizations," Empirical Economics, Springer, vol. 58(3), pages 1461-1490, March.
    10. Till Massing, 2018. "Simulation of Student–Lévy processes using series representations," Computational Statistics, Springer, vol. 33(4), pages 1649-1685, December.
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    12. Daniel T. Cassidy & Michael J. Hamp & Rachid Ouyed, 2013. "Log Student’s t -distribution-based option sensitivities: Greeks for the Gosset formulae," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1289-1302, July.
    13. Massing, Till & Ramos, Arturo, 2021. "Student’s t mixture models for stock indices. A comparative study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    14. Cassidy, Daniel T., 2011. "Describing n-day returns with Student’s t-distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(15), pages 2794-2802.
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