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Pricing European Options with a Log Student's t-Distribution: a Gosset Formula

Author

Listed:
  • Daniel T. Cassidy

    (McMaster University, Department of Engineering Physics, Hamilton, ON, Canada)

  • Michael J. Hamp

    (Scotiabank, Toronto, ON, Canada)

  • Rachid Ouyed

    (Department of Physics&Astronomy, University of Calgary, Calgary, AB, Canada and Origins Institute, McMaster University, Hamilton, ON, Canada)

Abstract

The distribution of the returns for a stock 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

  • Daniel T. Cassidy & Michael J. Hamp & Rachid Ouyed, 2009. "Pricing European Options with a Log Student's t-Distribution: a Gosset Formula," Papers 0906.4092, arXiv.org.
    • Handle: RePEc:arx:papers:0906.4092
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    References listed on IDEAS

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    1. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Lax, Melvin & Cai, Wei & Xu, Min, 2006. "Random Processes in Physics and Finance," OUP Catalogue, Oxford University Press, number 9780198567769.
    3. de Jong, C.M. & Huisman, R., 2000. "From Skews to a Skewed-t," ERIM Report Series Research in Management ERS-2000-12-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Daniel T. Cassidy & Michael J. Hamp & Rachid Ouyed, 2010. "Student's t-Distribution Based Option Sensitivities: Greeks for the Gosset Formulae," Papers 1003.1344, arXiv.org, revised Jul 2010.
    2. Higbee, Joshua D. & McDonald, James B., 2024. "A comparison of the GB2 and skewed generalized log-t distributions with an application in finance," Journal of Econometrics, Elsevier, vol. 240(2).

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