Multigrid method for a fully nonlinear Black-Scholes equation

Abstract

In this work, we present a multigrid approach for a fully nonlinear Black-Scholes equation arising in the modeling of markets frictions resulting from transaction costs. We consider a V-cycle method in order to minimize the computational cost of the numerical solution. The purpose of this paper is to show the effectiveness of multigrid approach for solving a fully nonlinear Black-Scholes problem.