Option Pricing with the Extreme Value Distributions by
نویسنده
چکیده
Recent events in financial markets have highlighted the frequency with which large scale financial losses occur. Extreme value theory focusses on the statistical properties of such extreme events. In this paper, extreme value distributions are applied in the context of option pricing. Analytic solutions to the standard European option problem based on the assumption that returns are Gumbel distributed are derived and found to perform better than the corresponding Black-Scholes solutions. The stochastic process underlying the Gumbel distribution is found to be a Lévy process and the Lévy characteristics of an approximating process are derived.
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