Clément, Emmanuelle; Lamberton, Damien; Protter, Philip An analysis of a least squares regression method for American option pricing. (English) Zbl 1039.91020 Finance Stoch. 6, No. 4, 449-471 (2002). 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. Reviewer: M. P. Moklyachuk (Kyïv) Cited in 2 ReviewsCited in 103 Documents MSC: 91G20 Derivative securities (option pricing, hedging, etc.) 93E20 Optimal stochastic control 60G40 Stopping times; optimal stopping problems; gambling theory Keywords:American options; optimal stopping; Monte Carlo methods; least squares regression PDFBibTeX XMLCite \textit{E. Clément} et al., Finance Stoch. 6, No. 4, 449--471 (2002; Zbl 1039.91020) Full Text: DOI