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

TL;DR

This paper introduces a novel fitted L-Multi-point Flux Approximation (L-MPFA) finite volume scheme for accurately pricing European and American options in two dimensions, effectively handling degeneracy in the Black-Scholes operator.

Contribution

The paper presents the first application of the fitted L-MPFA method for option pricing, combining it with upwind techniques to improve accuracy in degenerate diffusion problems.

Findings

The fitted L-MPFA method achieves high accuracy in numerical experiments.

The scheme effectively handles degeneracy in the Black-Scholes operator.

Numerical results compare favorably with existing methods.

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.