A Fixed Point Method for the Linear Complementarity Problem Arising from American Option Pricing

For American option pricing, the Black-Scholes-Merton model can be discretized as a linear complementarity problem (LCP) by using some finite difference schemes. It is well known that the Projected Successive Over Relaxation (PSOR) has been widely applied to solve the resulted LCP. In this paper, we propose a fixed point iterative method to solve this type of LCPs, where the splitting technique of the matrix is used. We show that the proposed method is globally convergent under mild assumptions. The preliminary numerical results are reported, which demonstrate that the proposed method is more accurate than the PSOR for the problems we tested.