## A stochastic mesh method for pricing high-dimensional American options (1997)

Venue: | Journal of Computational Finance |

Citations: | 88 - 6 self |

### BibTeX

@INPROCEEDINGS{Broadie97astochastic,

author = {Mark Broadie and Paul Glasserman},

title = {A stochastic mesh method for pricing high-dimensional American options},

booktitle = {Journal of Computational Finance},

year = {1997}

}

### Years of Citing Articles

### OpenURL

### Abstract

High-dimensional problems frequently arise in the pricing of derivative securities – for example, in pricing options on multiple underlying assets and in pricing term structure derivatives. American versions of these options, ie, where the owner has the right to exercise early, are particularly challenging to price. We introduce a stochastic mesh method for pricing high-dimensional American options when there is a finite, but possibly large, number of exercise dates. The algorithm provides point estimates and confidence intervals; we provide conditions under which these estimates converge to the correct values as the computational effort increases. Numerical results illustrate the performance of the method. 1

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Citation Context ...ion density f of the underlying state variables is known or can be evaluated numerically. In practice, complicated diffusions are usually simulated using an Euler discretization (as described in, eg, =-=Kloeden and Platen, 1999-=-) with simpler transition densities approximating the true transition densities, and these can be used in the mesh. An alternative strategy for selecting weights that avoids densities entirely is prop... |

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Citation Context ...lation with regression on a set of basis functions to develop low-dimensional approximations to high-dimensional dynamic programs, in the same spirit as some deterministic numerical methods (see, eg, =-=Judd, 1998-=-). As explained in Section 8.6.2 of Glasserman (2004), those methods are related to the stochastic mesh introduced here and correspond to an implicit choice of mesh weights. The stochastic mesh method... |

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Citation Context ...he computational work is quadratic in the number of time steps, the convergence rate for the binomial method is O(work –1⁄2 ). All of the multi-dimensional generalizations of the binomial method (eg, =-=Boyle, Evnine, and Gibbs, 1989-=-; He, 1990; and Kamrad and Ritchken, 1991) have work which increases as m n + 1 , where m is the number of time steps and n is the number Volume 7/Number 4, Summer 2004 URL: www.thejournalofcomputatio... |

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Citation Context ...er of time steps, the convergence rate for the binomial method is O(work –1⁄2 ). All of the multi-dimensional generalizations of the binomial method (eg, Boyle, Evnine, and Gibbs, 1989; He, 1990; and =-=Kamrad and Ritchken, 1991-=-) have work which increases as m n + 1 , where m is the number of time steps and n is the number Volume 7/Number 4, Summer 2004 URL: www.thejournalofcomputationalfinance.coms60 Mark Broadie and Paul G... |

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Citation Context ...ic in the number of time steps, the convergence rate for the binomial method is O(work –1⁄2 ). All of the multi-dimensional generalizations of the binomial method (eg, Boyle, Evnine, and Gibbs, 1989; =-=He, 1990-=-; and Kamrad and Ritchken, 1991) have work which increases as m n + 1 , where m is the number of time steps and n is the number Volume 7/Number 4, Summer 2004 URL: www.thejournalofcomputationalfinance... |

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