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August 2007 A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options
Daniel Egloff, Michael Kohler, Nebojsa Todorovic
Ann. Appl. Probab. 17(4): 1138-1171 (August 2007). DOI: 10.1214/105051607000000249

Abstract

Under the assumption of no-arbitrage, the pricing of American and Bermudan options can be casted into optimal stopping problems. We propose a new adaptive simulation based algorithm for the numerical solution of optimal stopping problems in discrete time. Our approach is to recursively compute the so-called continuation values. They are defined as regression functions of the cash flow, which would occur over a series of subsequent time periods, if the approximated optimal exercise strategy is applied. We use nonparametric least squares regression estimates to approximate the continuation values from a set of sample paths which we simulate from the underlying stochastic process. The parameters of the regression estimates and the regression problems are chosen in a data-dependent manner. We present results concerning the consistency and rate of convergence of the new algorithm. Finally, we illustrate its performance by pricing high-dimensional Bermudan basket options with strangle-spread payoff based on the average of the underlying assets.

Citation

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Daniel Egloff. Michael Kohler. Nebojsa Todorovic. "A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options." Ann. Appl. Probab. 17 (4) 1138 - 1171, August 2007. https://doi.org/10.1214/105051607000000249

Information

Published: August 2007
First available in Project Euclid: 10 August 2007

zbMATH: 1136.91010
MathSciNet: MR2344302
Digital Object Identifier: 10.1214/105051607000000249

Subjects:
Primary: 60G40, 91B28, 93E20
Secondary: 62G05, 65C05, 93E24

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.17 • No. 4 • August 2007
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