Primal‐dual active set algorithm for valuating American options under regime switching

Abstract

This paper focuses on numerical algorithms to value American options under regime switching. The prices of such options satisfy a set of complementary parabolic problems on an unbounded domain. Based on our previous experience, the pricing model could be truncated into a linear complementarity problem (LCP) over a bounded domain. In addition, we transform the resulting LCP into an equivalent variational problem (VP), and discretize the VP by an Euler‐finite element method. Since the variational matrix in the discretized system is P‐matrix, a primal‐dual active set (PDAS) algorithm is proposed to evaluate the option prices efficiently. As a specialty of PDAS, the optimal exercise boundaries in all regimes are obtained without further computation cost. Finally, numerical simulations are carried out to test the performance of our proposed algorithm and compare it to existing methods.