A SECOND-ORDER TRIDIAGONAL METHOD FOR AMERICAN OPTIONS UNDER JUMP-DIFFUSION MODELS

Abstract

We propose an implicit numerical method for pricing American options where the underlying asset follows a jump-diffusion model. Using the fact that the prices of American options are given by linear complementarity problems (LCPs), we combine an implicit finite difference method with an operator splitting method. The proposed method is constructed on three time levels, and the operator splitting method is used to treat American constraints. We concentrate on the formulation of the numerical method which leads to linear systems with tridiagonal coefficient matrices. Numerical experiments show that the implicit method has the second-order convergence rate, and the prices of American options can be obtained in a fraction of a second on a computer.