High-Order Compact Finite Difference Scheme for Pricing Asian Option with Moving Boundary Condition

Abstract

In this paper, an unconditionally stable compact finite difference scheme for the solution of linear convection–diffusion equation is proposed. In the proposed scheme, second derivative approximations of the unknowns are eliminated with the unknowns itself and their first derivative approximations while retaining the fourth order accuracy and tri-diagonal nature of the scheme. Proposed compact finite difference scheme which is fourth order accurate in spatial variable and second or lower order accurate in temporal variable depending on the choice of weighted time average parameter is applied to Asian option partial differential equation. A diagonally dominant system of linear equation is obtained from the proposed scheme which can be efficiently solved. Two numerical examples are given to demonstrate the efficiency and accuracy of the proposed compact finite difference scheme.