  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.
