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

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.