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