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

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

2009-06-22

arxiv.org/abs/0906.4092v1

Economy

Quantitative Finance

Pricing of Securities

12 journal pages, 9 figures and 3 tables (Submitted to Physica A)

Scientific paper

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.

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