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Student's t-Distribution Based Option Sensitivities: Greeks for the Gosset Formulae

Author

Listed:
  • Daniel T. Cassidy

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

  • Michael J. Hamp

    (Scotiabank, Toronto, Ontario, Canada)

  • Rachid Ouyed

    (Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, Canada)

Abstract

European options can be priced when returns follow a Student's t-distribution, provided that the asset is capped in value or the distribution is truncated. We call pricing of options using a log Student's t-distribution a Gosset approach, in honour of W.S. Gosset. In this paper, we compare the greeks for Gosset and Black-Scholes formulae and we discuss implementation. The t-distribution requires a shape parameter \nu to match the "fat tails" of the observed returns. For large \nu, the Gosset and Black-Scholes formulae are equivalent. The Gosset formulae removes the requirement that the volatility be known, and in this sense can be viewed as an extension of the Black-Scholes formula.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1003.1344
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    References listed on IDEAS

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