Primal-dual active set algorithm for valuating American options under regime switching (Q6590575)

In this article, an efficient numerical method is proposed for evaluating American options under regime switching. The prices of such options satisfy a set of complementary parabolic problems on an unbounded domain. A bounded linear complementarity problem (LCP) related to options is presented by using some numerical transformations and the a priori information of original pricing model. An Euler-finite element method has been established to discretize the variational problem corresponding to the resulting LCP. Based on the property that the discretized matrix is a P-matrix, a primal-dual active set (PDAS) algorithm is employed, which calculates the option prices and the optimal exercise boundaries in all regimes simultaneously. Numerical experiments are conducted in Section 4 to illustrate the effectiveness of the proposed approach.