Nonparametric econometrics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Regression methods for pricing complex American-style options
IEEE Transactions on Neural Networks
An irregular grid method for high-dimensional free-boundary problems in finance
Future Generation Computer Systems - Special issue: Selected numerical algorithms
The valuation of multidimensional American real options using the LSM simulation method
Computers and Operations Research
An irregular grid approach for pricing high-dimensional American options
Journal of Computational and Applied Mathematics
An efficient implementation of a least squares Monte Carlo method for valuing American-style options
International Journal of Computer Mathematics - SPECIAL ISSUE ON FINANCIAL DERIVATIVES
Valuing Modularity as a Real Option
Management Science
American option pricing with randomized quasi-Monte Carlo simulations
Proceedings of the Winter Simulation Conference
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In a recent paper, Longstaff and Schwartz (2001) suggest a method to American option valuation based on simulation. The method is termed the Least Squares Monte Carlo (LSM) method, and although it has become widely used, not much is known about the properties of the estimator. This paper corrects this shortcoming using theory from the literature on seminonparametric series estimators. A central part of the LSM method is the approximation of a set of conditional expectation functions. We show that the approximations converge to the true expectation functions under general assumptions in a multiperiod, multidimensional setting. We obtain convergence rates in the two-period, multidimensional case, and we discuss the relation between the optimal rate of convergence and the properties of the conditional expectation. Furthermore, we show that the actual price estimates converge to the true price. This provides the mathematical foundation for the use of the LSM method in derivatives research.