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Log Student’s t -distribution-based option sensitivities: Greeks for the Gosset formulae

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

Abstract

European options can be priced when returns follow a log 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 to match the ‘fat tails’ of the observed log returns. For large , the Gosset and Black--Scholes formulae are equivalent. The Gosset formula removes the requirement that the volatility be known, and in this sense can be viewed as an extension of the Black--Scholes formula.

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  • 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.
    • Handle: RePEc:taf:quantf:v:13:y:2013:i:8:p:1289-1302
    DOI: 10.1080/14697688.2012.744087
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    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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