Primal-dual active set method for evaluating American put options on zero-coupon bonds

An efficient numerical method is propoesd for a parabolic linear complementarity problem (LCP) arising in the valuation of American options on zero-coupon bonds under the Cox-Ingersoll-Ross (CIR) model. With variable substitutions, we first transform the original pricing problem into a degenerated linear complementarity problem on a bounded domain, and present a corresponding variational inequality (VI). We then give the full discretization scheme of VI constructed by finite element and finite difference methods in spatial and temporal directions, respectively. Within the framework of VI, the stability and the rate of convergence are obtained. Moreover, for the resulted discretised variational inequality, we present a primal-dual active set (PDAS) method to solve it. Numerical results are carried out to test the usefulness of the proposed method compared with existing methods.