On Stability and Convergence of a Finite Difference Approximation to a Parabolic Variational Inequality Arising From American Option Valuation

Abstract

In this article we study the numerical solution of a degenerate variational inequality of parabolic type arising from the valuation of American options by a finite difference method. Stability and convergence of the finite difference method are established. Numerical results are also presented to show the effectiveness and usefulness of the discretization scheme.