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Monte Carlo Valuation of American Options through Computation of the Optimal Exercise Frontier

Published online by Cambridge University Press:  06 April 2009

Alfredo Ibáñez  and
Fernando Zapatero
Alfredo Ibáñez
Affiliation:
[email protected], Departamento de Administración, Instituto Tecnológico Autónomo de Mexico, Río Hondo #1, Mexico DF 01000 (Mexico)
Fernando Zapatero
Affiliation:
[email protected], Finance and Business Economics Department, Marshall School of Business, University of Southern California, Los Angeles, CA 90089.
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Abstract

This paper introduces a Monte Carlo simulation method for pricing multidimensional American options based on the computation of the optimal exercise frontier. We consider Bermudan options that can be exercised at a finite number of times and compute the optimal exercise frontier recursively. We show that for every date of possible exercise, any single point of the optimal exercise frontier is a fixed point of a simple algorithm. Once the frontier is computed, we use plain vanilla Monte Carlo simulation to price the option and obtain a low-biased estimator. We illustrate the method with applications to several types of options.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 39 , Issue 2 , June 2004 , pp. 253 - 275
Copyright
Copyright © School of Business Administration, University of Washington 2004

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