Pricing High-Dimensional American Options Using the Stochastic Grid Method
31 Pages Posted: 12 Dec 2010 Last revised: 21 Feb 2012
Date Written: December 18, 2010
This paper considers the problem of pricing options with early-exercise features whose pay-off depends on several sources of uncertainty. We propose a stochastic grid method for estimating the optimal exercise policy and using this policy to obtain a low-biased estimator for high-dimensional American options. The method has elements of the least squares method (LSM) of Longstaff and Schwartz (2001), the stochastic mesh method of Broadie and Glasserman (2004), and stratified state aggregation along the pay-off method of Barraquand and Martineau (1995), with certain distinct advantages over the existing methods. Numerical results are given for single asset Bermudan options, Bermudan max options, Bermudan options on the arithmetic mean of a collection of stocks.
Keywords: American Options, High Dimensional, Stochastic Grid Method, Regression, Monte Carlo, SSAP, LSM, Bermudan, Gram Charlier
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