Analysis of the SSAP Method for the Numerical Valuation of High-Dimensional Multivariate American Securities

Abstract.

We consider a new numerical method developed by Barraquand and Martineau for the pricing of American securities where the payoff depends on several sources of uncertainty. This method utilizes Monte Carlo simulation and is referred to as Stratified State Aggregation along the Payoff (SSAP). Since there are no other methods that so effectively reduce the dimensionality of high-dimensional problems, the SSAP method has generated significant interest. Numerical results are presented showing that, if a sufficiently large number of time steps are used, in the cases of the two-dimensional maximum and minimum options, SSAP typically prices to within 6 cents of the true price. However, we show that if the security depends on two or more sources of uncertainty, then the price obtained by the SSAP method will not, in general, converge to the correct theoretical price, due in large part to incorrect exercise decisions being made. We analyze the exercise regions in the cases of the two-dimensional maximum and minimum options and show how SSAP makes incorrect exercise decisions. Suggestions for improving SSAP pricing accuracy by choosing a partition other than the payoff are discussed.