Option pricing via Monte Carlo simulation – a weak derivative approach

Option pricing via Monte Carlo simulation – a weak derivative approach

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Article ID: iaor20023300
Country: United States
Volume: 15
Issue: 3
Start Page Number: 335
End Page Number: 349
Publication Date: Jan 2001
Journal: Probability in the Engineering and Informational Sciences
Authors:
Keywords: option pricing
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 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.

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