Applications Of Primal-Dual Active Set Method For Pricing American Outer Performance Options

The American outer performance option studied in this paper is a rainbow option based on two underlying assets.Its pricing model can be described by a parabolic variational inequality equation in a two-dimensional unbounded region,which is also a two-dimensional free boundary problem.Based on dimensionality reduction,far-field truncation technique,prior estimation of free boundary,and some variable substitutions,we transform the original pricing model into a parabolic linear complementarity problem(LCP)over a onedimensional bounded region,and give its corresponding variational problem(VI).Furthermore,finite difference method and finite element method are used for numerical discretization in time and space directions respectively,and the order of convergence is estimated.Then,according to the characteristics of the corresponding algebraic system after discretization,a primal-dual active set method(PDAS)is designed to solve the problem,and the option price and the optimal exercise boundary are obtained simultaneously.Finally,the correctness and effectiveness of the proposed algorithm are verified by multiple numerical simulations.