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

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