A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options
Egloff, Daniel ; Kohler, Michael ; Todorovic, Nebojsa
Ann. Appl. Probab., Tome 17 (2007) no. 1, p. 1138-1171 / Harvested from Project Euclid
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/