Numerical Valuation of High Dimensional Multivariate American Securities

We consider the problem of pricing an American contingent claim whose payoff depends on several sources of uncertainty. Several efficient numerical lattice-based techniques exist for pricing American securities depending on one or few (up to three) risk sources. However, these methods cannot be used for high dimensional problems, since their memory requirement is exponential in the number of risk sources. We present an efficient numerical technique that combines Monte Carlo simulation with a particular partitioning method of the underlying assets space, which we call Stratified State Aggregation (SSA). Using this technique, we can compute accurate approximations of prices of American securities with an arbitrary number of underlying assets. Our numerical experiments show that the method is practical for pricing American claims depending on up to 400 risk sources.