A STATE‐SPACE PARTITIONING METHOD FOR PRICING HIGH‐DIMENSIONAL AMERICAN‐STYLE OPTIONS

Abstract

The pricing of American‐style options by simulation‐based methods is an important but difficult task primarily due to the feature of early exercise, particularly for high‐dimensional derivatives. In this paper, a bundling method based on quasi‐Monte Carlo sequences is proposed to price high‐dimensional American‐style options. The proposed method substantially extends Tilley's bundling algorithm to higher‐dimensional situations. By using low‐discrepancy points, this approach partitions the state space and forms bundles. A dynamic programming algorithm is then applied to the bundles to estimate the continuation value of an American‐style option. A convergence proof of the algorithm is provided. A variety of examples with up to 15 dimensions are investigated numerically and the algorithm is able to produce computationally efficient results with good accuracy.

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