infonet-economy

In this paper, a new technique for pricing of European and American Parisian options, that we call the québécoisation method, is developed. We study the pricing of Parisian options in a hyper-exponential jump-diffusion model using the double Laplace-Carson transform with respect to the time to maturity and the residual Parisian time (time to expiration of the Parisian window) of the system of two partial integro-differential equations describing the option price dynamics. The transformed, i.e., québécoised, option price and hedging parameters delta and gamma are computed in a closed form, and the final results are obtained via the two-dimensional Gaver-Stehfest inversion algorithm. Our pricing method is analytically tractable, and it provides important economic insights for pricing and hedging of European and American Parisian options in the presence of jumps.