arXiv subjects

Michael J. Hamp

Publications and source records attributed to Michael J. Hamp.

2 recordsLinked to original sources

arXiv2010

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

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 νto match the "fat tails" of the observed returns. For large ν, 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.

q-fin.PR↗

arXiv2009

Pricing European Options with a Log Student's t-Distribution: a Gosset Formula

The distribution of the returns for a stock are not well described by a normal probability density function (pdf). Student's t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of European call or put options using a log Student's t-distribution, which we call a Gosset approach in honour of W.S. Gosset, the author behind the nom de plume Student. The approach that we present can be used to price European options using other distributions and yields the Black-Scholes formula for returns described by a normal pdf.

q-fin.PR↗