Primal-dual active set method for pricing American better-of option on two assets

Abstract

An American better-of option is a rainbow option with two underlying assets. It can be described by a parabolic variational inequality (VI) on a two-dimensional unbounded domain, which can also be characterized by a two-dimensional free boundary problem. Based on the numeraire transformation and the known information on the free boundary, we derive a one-dimensional linear complementarity problem (LCP) related to options on a bounded domain. Moreover, the full discretization scheme of LCP is constructed by finite difference and finite element methods in temporal and spatial directions, respectively. The primal-dual active-set (PDAS) method is adopted for solving the resulting large-scale discretized system. In each PDAS iteration, a unique index set of primal-dual variables will be computed by solving a linear system. A systematical convergent analysis is presented on our proposed method for pricing American better-of options. One of the desirable features of our method is that we can get the option value and two free boundaries simultaneously. Numerical simulations are performed to verify the efficiency of our proposed method.