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

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

2010-03-06

arxiv.org/abs/1003.1344v2

Economy

Quantitative Finance

Pricing of Securities

28 pages, 14 figures and 6 tables. Follow-up to the arXiv:0906.4092 work/paper

Scientific paper

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.

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