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An analysis of a least squares regression method for American option pricing. (English) Zbl 1039.91020
The authors analyze the least squares regression method computing the American option prices proposed by F. A. Longstaff and E. S. Schwartz [Rev. Financial Stud. 14, 113–148 (2001)]. Two types of approximation are involved in the proposed algorithm. Approximation one: replace the conditional expectations in the dynamic programming principle by projections on a finite set of functions. Approximation two: use Monte-Carlo simulations and least squares regression to compute the value function of approximation one. The almost sure convergence of the complete algorithm is proved under some general conditions. A type of the central limit theorem for the rate of convergence of the Monte-Carlo procedure is proved, thus providing the normalized error is asymptotically Gaussian.

91G20 Derivative securities (option pricing, hedging, etc.)
93E20 Optimal stochastic control
60G40 Stopping times; optimal stopping problems; gambling theory
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