Numerical Valuation of High Dimensional Multivariate American Securities

This work presents an efficient numerical technique that combines Monte Carlo simulation with a particular partitioning method of the underlying assets space, which is called Stratified State Aggregation (SSA), which can compute accurate approximations of prices of American securities with an arbitrary number of underlying assets.

Abstract

We consider the problem of pricing an American contingent claim whose payoff depends on several sources of uncertainty.Using classical assumptions from the Arbitrage Pricing Theory, the theoretical price can be computed as the maximum over all possible early exercise strategies of the discounted expected cash flows under the modified risk-neutral information process.Several efficient numerical techniques exist for pricing American securities depending on one or few (up to 3) risk sources.They are either lattice-based techniques or finite difference approximations of the Black-Scholes diffusion equation.However, these methods cannot be used for high-dimensional problems, since their memory requirement is exponential in the number of risk sources.