The Annals of Applied Probability

A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options

Daniel Egloff, Michael Kohler, and Nebojsa Todorovic

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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.

Article information

Ann. Appl. Probab., Volume 17, Number 4 (2007), 1138-1171.

First available in Project Euclid: 10 August 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 91B28 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 93E20: Optimal stochastic control
Secondary: 65C05: Monte Carlo methods 93E24: Least squares and related methods 62G05: Estimation

Optimal stopping American options Bermudan options nonparametric regression Monte Carlo methods


Egloff, Daniel; Kohler, Michael; Todorovic, Nebojsa. A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options. Ann. Appl. Probab. 17 (2007), no. 4, 1138--1171. doi:10.1214/105051607000000249.

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