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Sensitivity Analysis for Monte Carlo Simulation of Option Pricing

Published online by Cambridge University Press:  27 July 2009

Michael C. Fu  and
Jian-Qlang Hu
Michael C. Fu
Affiliation:
College of Business and Management, University of Maryland, College Park, Maryland 20742
Jian-Qlang Hu
Affiliation:
Department of Manufacturing Engineering, Boston University, 44 Cummington Street, Boston, Massachusetts 02215
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Abstract

Monte Carlo simulation is one alternative for analyzing options markets when the assumptions of simpler analytical models are violated. We introduce techniques for the sensitivity analysis of option pricing, which can be efficiently carried out in the simulation. In particular, using these techniques, a single run of the simulation would often provide not only an estimate of the option value but also estimates of the sensitivities of the option value to various parameters of the model. Both European and American options are considered, starting with simple analytically tractable models to present the idea and proceeding to more complicated examples. We then propose an approach for the pricing of options with early exercise features by incorporating the gradient estimates in an iterative stochastic approximation algorithm. The procedure is illustrated in a simple example estimating the option value of an American call. Numerical results indicate that the additional computational effort required over that required to estimate a European option is relatively small.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 3 , July 1995 , pp. 417 - 446
Copyright
Copyright © Cambridge University Press 1995

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