Pricing High-Dimensional American Options Using the Stochastic Grid Method

31 Pages Posted: 12 Dec 2010 Last revised: 21 Feb 2012

See all articles by Shashi Jain

Shashi Jain

Indian Institute of Science (IISc) - Deptartment of Management Studies

Cornelis W. Oosterlee

Center for Mathematics and Computer Science (CWI)

Date Written: December 18, 2010

Abstract

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

Suggested Citation

Jain, Shashi and Oosterlee, Cornelis W., Pricing High-Dimensional American Options Using the Stochastic Grid Method (December 18, 2010). Available at SSRN: https://ssrn.com/abstract=1723712 or http://dx.doi.org/10.2139/ssrn.1723712

Shashi Jain

Indian Institute of Science (IISc) - Deptartment of Management Studies ( email )

Indian Institute of Science
Bangalore
India

Cornelis W. Oosterlee (Contact Author)

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

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