Pricing American Stock Options by Linear Programming

We investigate numerical solution of finite difference approximations to American option pricing problems, using a novel direct numerical method --- simplex solution of a linear programming formulation. This approach is based on a new result extending to the parabolic case the equivalence between linear order complementarity problems and abstract linear programmes known for certain elliptic operators. We test this method empirically, comparing simplex and interior point algorithms with the projected successive overrelaxation (PSOR) algorithm applied to the American vanilla put and lookback put. We conclude that simplex is roughly comparable with projected SOR on average (faster for fine discretisations, slower for coarse), but is more desirable for robustness of solution time under changes in parameters. Furthermore, significant speed-ups are certainly possible over the results given here.