A more accurate finite difference approach to the pricing of contingent claims

Abstract

Numerical approximations of contingent claim partial differential equations (PDEs) are quickly becoming one of the most accepted techniques used in derivative security valuation. The most common methodology is the finite difference method (FDM). This procedure can be used as long as a well-posed PDE can be derived and therefore lends itself to contingent claims. The FDM requires prescribed conditions at the boundary. These boundary conditions are not readily available (at all boundaries) for most contingent claim PDEs. This study presents an accurate and computationally inexpensive method for providing these boundary conditions. These absorbing and adjusting boundary conditions when applied to the contingent claim PDEs presented in this study increased the accuracy of the FDM solution at relatively little cost.