Barycentric spectral domain decomposition methods for valuing a class of infinite activity Lévy models

Abstract

A new barycentric spectral domain decomposition methods algorithm for solving partial integro-differential models is described. The method is applied to European and butterfly call option pricing problems under a class of infinite activity Lévy models. It is based on the barycentric spectral domain decomposition methods which allows the implementation of the boundary conditions in an efficient way. After the approximation of the spatial derivatives, we obtained the semi-discrete equations. The computation of these equations is performed by using the barycentric spectral domain decomposition method. This is achieved with the implementation of an exponential time integration scheme. Several numerical tests for the pricing of European and butterfly options are given to illustrate the efficiency and accuracy of this new algorithm. We also show that Greek options, such as Delta and Gamma sensitivity, are computed with no spurious oscillation.