An Efficient Fourth-Order Numerical Scheme for Nonlinear Multi-asset Option Pricing Problems

This paper proposes a fourth-order numerical scheme for solving multi-asset nonlinear variable coefficient Black-Scholes PDEs. First, using the Newton linearization technique, we linearize the given nonlinear PDE, and obtain a sequence of linear PDEs. Then, we discretize the time derivative by the Crank-Nicolson scheme, and the resultant semi-discrete problem by the central difference scheme on uniform meshes. In order to enhance the order of convergence of the proposed scheme, we use the Richardson extrapolation method, by solving the fully discrete problem on two different meshes. The stability and convergence are studied. To validate the proposed technique, several numerical experiments are carried out.