Projection and contraction method for the valuation of American options under regime switching

Abstract

This paper proposes an efficient numerical algorithm to evaluate American put options under regime switching. A set of variational inequalities could describe the pricing model, which is equivalent to a coupled parabolic free boundary problem. With variable substitutions and truncation techniques, the original pricing problem is transformed into a coupled linear complementarity problem on a bounded rectangular domain. Then, the variational problem related to the linear complementary problem is obtained. Furthermore, a finite difference method in the temporal direction and a finite element method in the spatial direction lead to a full-discretized approximation of the variational problem. Based on the positive definiteness of the discretized matrix, a projection and contraction method is adopted for the resulting discretized variational problem. Finally, several numerical simulations are carried out to illustrate the efficiency of the proposed method compared with existing methods.