A Positive Flux Limited Difference Scheme for Option Pricing 2D Fully Non-linear Parabolic Equation with Uncertain Correlation

Miglena N. Koleva; Lubin G. Vulkov

doi:10.1016/j.cam.2015.02.054

paper

A Positive Flux Limited Difference Scheme for Option Pricing 2D Fully Non-linear Parabolic Equation with Uncertain Correlation

arXiv:1404.2459 · doi:10.1016/j.cam.2015.02.054

Abstract

We consider a two-asset non-linear model of option pricing in an environment where the correlation is not known precisely, but varies between two known values. First we discuss the non-negativity of the solution of the equation. Next, we construct and analyze a positivity preserving, flux-limited difference scheme for the corresponding boundary value problem. Numerical experiments are analyzed.