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The Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing

Markose, Sheri M and Alentorn, Amadeo (2005) The Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing. Working Paper. University of Essex Department of Economics Discussion Papers.

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Abstract

Crisis events such as the 1987 stock market crash, the Asian Crisis and the bursting of the Dot-Com bubble have radically changed the view that extreme events in financial markets have negligible probability. This paper argues that the use of the Generalized Extreme Value (GEV) distribution to model the Risk Neutral Density (RND) function provides a flexible framework that captures the negative skewness and excess kurtosis of returns, and also delivers the market implied tail index of asset returns. We obtain an original analytical closed form solution for the Harrison and Pliska (1981) no arbitrage equilibrium price for the European option in the case of GEV asset returns. The GEV based option prices successfully remove the well known pricing bias of the Black-Scholes model. We explain how the implied tail index is efficacious at identifying the fat tailed behaviour of losses and hence the left skewness of the price RND functions, particularly around crisis events.

Item Type: Monograph (Working Paper)
Subjects: H Social Sciences > HB Economic Theory
Divisions: Faculty of Social Sciences > Economics, Department of
Depositing User: Jim Jamieson
Date Deposited: 16 Aug 2012 13:55
Last Modified: 28 Aug 2014 11:46
URI: http://repository.essex.ac.uk/id/eprint/3726

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