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.
Publié le : 2007-08-14
Classification:
Optimal stopping,
American options,
Bermudan options,
nonparametric regression,
Monte Carlo methods,
91B28,
60G40,
93E20,
65C05,
93E24,
62G05
@article{1186755235,
author = {Egloff, Daniel and Kohler, Michael and Todorovic, Nebojsa},
title = {A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options},
journal = {Ann. Appl. Probab.},
volume = {17},
number = {1},
year = {2007},
pages = { 1138-1171},
language = {en},
url = {http://dml.mathdoc.fr/item/1186755235}
}
Egloff, Daniel; Kohler, Michael; Todorovic, Nebojsa. A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options. Ann. Appl. Probab., Tome 17 (2007) no. 1, pp. 1138-1171. http://gdmltest.u-ga.fr/item/1186755235/