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OPTION PRICING VIA MONTE CARLO SIMULATION

A WEAK DERIVATIVE APPROACH

Published online by Cambridge University Press:  27 July 2001

Bernd Heidergott
Bernd Heidergott
Affiliation:
EURANDOM, 5600 MB Eindhoven, The Netherlands, E-mail: [email protected]
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Abstract

Using a weak derivation approach to gradient estimation, we consider the problem of pricing an American call option on stock paying dividends at discrete times. Similar simulation-based sensitivity estimators were introduced earlier by Fu and Hu (1995) who used smoothed perturbation analysis. We improve upon their results by presenting an estimator with a uniformly lower variance. In addition, we reduced the multidimensional optimization problem of pricing an option with multiple ex-dividend dates to a one-dimensional one. Numerical examples indicate that this approach saves a considerable amount of computation time. Our estimator holds uniformly for a class of payoff functions, and applications to other types of options will be addressed in the article.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 15 , Issue 3 , July 2001 , pp. 335 - 349
Copyright
© 2001 Cambridge University Press

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