Fourth-Order Compact Finite Difference Scheme for American Option Pricing Under Regime-Switching Jump-Diffusion Models

In this paper, a fourth-order compact finite difference scheme is proposed for the solution of partial integro-differential equation arising in option pricing under jump-diffusion models. In proposed compact 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. We use the proposed compact scheme with three time levels along with operator splitting technique to solve the linear complementary problem which arises in American option pricing under regime-switching jump-diffusion models. Moreover, it is shown that the proposed scheme leads to a tri-diagonal system of linear equations and fourth order accuracy is obtained. Since initial condition is not smooth enough for jump-diffusion model, we employ the smoothing operators to ensure high-order convergence rate. Numerical examples for American option pricing under Merton and Kou regime-switching jump-diffusion models are given. © 2017, Springer India Pvt. Ltd.