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

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

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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.

Date: 2010-03, Revised 2010-07
New Economics Papers: this item is included in nep-rmg
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