Pricing high-dimensional Bermudan options using the stochastic grid method

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 use this policy to obtain a low-biased estimator for high-dimensional Bermudan options. The method has elements of the least-squares method (LSM) of Longstaff and Schwartz [Valuing American options by simulation: A simple least-squares approach, Rev. Finan. Stud. 3 (2001), pp. 113–147], the stochastic mesh method of Broadie and Glasserman [A stochastic mesh method for pricing high-dimensional American option, J. Comput. Finance 7 (2004), pp. 35–72], and stratified state aggregation along the pay-off method of Barraquand and Martineau [Numerical valuation of high-dimensional multivariate American securities, J. Financ. Quant. Anal. 30 (1995), pp. 383–405], with certain distinct advantages over the existing methods. We focus on the numerical results for high-dimensional problems such as max option and arithmetic basket option on several assets, with basic error analysis for a general one-dimensional problem.