Pricing Contingent Claims with an Underlying Asset Driven by an Extreme Value Distribution : Options on Dow Jones Industrial Average Index, 2009-2010

This paper is aimed to develop an equilibrium model in a stochastic economy populated by identical, competitive, and risk-averse consumers (investors), to value a European call option on stock whose price is subject to extreme and unexpected jumps. It is assumed that the underlying asset price is driven by a mixed jump-diffusion process with the jump size following an extreme value type distribution. The option price is characterized by a differential-integral equation with boundary conditions; an analytical solution for such a characterization is provided. Finally, a Monte Carlo simulation, with market daily data, is carried out to obtain numerical approximations of call options on the Dow Jones Industrial Average Index during the period 2009-2010