A fitted L-Multi-point Flux Approximation method for pricing options

Abstract

In this paper, we introduce a special kind of finite volume method called Multi-Point Flux Approximation method (MPFA) to price European and American options in two dimensional domain. We focus on the L-MPFA method for space discretization of the diffusion term of Black-Scholes operator. The degeneracy of the Black Scholes operator is tackled using the fitted finite volume method. This combination of fitted finite volume method and L-MPFA method coupled to upwind methods gives us a novel scheme called the fitted L-MPFA method. Numerical experiments show the accuracy of the novel fitted L-MPFA method comparing to well known schemes for pricing options.