Pricing European options with a log Student’s t-distribution: A Gosset formula

The distributions of returns for stocks 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,...

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Bibliographic Details
Published in:Physica A 2010-12, Vol.389 (24), p.5736-5748
Main Authors: Cassidy, Daniel T., Hamp, Michael J., Ouyed, Rachid
Format: Article
Language:English
Subjects:
Econophysics
European options
Fat-tailed distributions
Financial risk
Plumes
Pricing
Probability density functions
Raw materials
Statistical mechanics
Students
Student’s [formula omitted]-distribution
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Summary:The distributions of returns for stocks 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.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2010.08.037