Pricing multi-dimension American options by simulation

Abstract

Applying Monte Carlo Simulation to American option is very hard and was considered impossible. The cash flow of American options not only depends on the price path of the underlying assets but also depends on the decisions of the option holder. Our algorithm is based on State-Space Partitioning Method. The main challenge in using this kind of methods is the selection of the state-space partitions. The low-discrepancy sequences, such as Sobol sequence, can fill in the spacequickly in an efficient way. The algorithm we present here uses low-discrepancy sequences as "Representative State" to partition the state-space, so that we can deal with the pricing in high dimensions.