A sliced-finite difference method for the American option

Abstract

It is generally accepted that the Black-Scholes model for American option pricing is a free-boundary problem involving a partial differential equation. Approximate solutions may be obtained using numerical methods, but the precision and stability of these solutions is hard to control since they are significantly affected by the singularity at the exercise boundary near the expiration date. We propose a Sliced-Finite Difference (SFD) numerical method, to solve the pricing problem of American put options. The proposed method combines the advantages of the semi-analytical method and the sliced-fixed boundary finite difference method and overcomes their deficiencies. Using the SFD method, we can resolve the problem that results from the singularity near the optimal exercise boundary. Numerical experiments show that the SFD method is more accurate than other numerical methods. The proposed method is targeted at American put options but it is also applicable to other types of options.