# A Fitted Multi-Point Flux Approximation Method for Pricing two options

## TL;DR

This paper introduces novel numerical schemes based on Multi-Point Flux Approximation (MPFA) for accurately pricing two-asset options by effectively handling PDE degeneracy and improving upon existing methods.

## Contribution

The paper develops a fitted MPFA method combined with upwinding and $ heta$-Euler time discretization, offering enhanced accuracy over current fitted finite volume approaches.

## Key findings

- Fitted MPFA scheme outperforms existing methods in accuracy.
- Numerical simulations validate the effectiveness of the new schemes.
- The methods handle PDE degeneracy efficiently on non-uniform grids.

## Abstract

In this paper, we develop novel numerical methods based on the Multi-Point Flux Approximation (MPFA) method to solve the degenerated partial differential equation (PDE) arising from pricing two-assets options. The standard MPFA is used as our first method and is coupled with a fitted finite volume in our second method to handle the degeneracy of the PDE and the corresponding scheme is called fitted MPFA method. The convection part is discretized using the upwinding methods (first and second order) that we have derived on non uniform grids. The time discretization is performed with $\theta$- Euler methods. Numerical simulations show that our new schemes can be more accurate than the current fitted finite volume method proposed in the literature.