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arXiv · 0710.3640

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

Daniel Egloff·Michael Kohler·Nebojsa Todorovic
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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.

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Daniel Egloff, Michael Kohler, Nebojsa Todorovic. 2007-10-19. A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options. https://doi.org/10.1214/105051607000000249

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