Pricing High-Dimensional American Options Using Local Consistency Conditions

We investigate a new method for pricing high-dimensional American options. The method is of ???nite di???erence type but is also related to Monte Carlo techniques in that it involves a representative sampling of the underlying variables. An approximating Markov chain is built using this sampling and linear programming is used to satisfy local consistency conditions at each point related to the in???nitesimal generator or transition density. The algorithm for constructing the matrix can be parallelised easily, moreover once it has been obtained it can be reused to generate quick solutions for a wide range of related problems. We provide pricing results for geometric average options in up to ten dimensions, and compare these to accurate benchmarks.