American option pricing under stochastic volatility: an efficient numerical approach

American option pricing under stochastic volatility: an efficient numerical approach

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Article ID: iaor20101476
Volume: 7
Issue: 2
Start Page Number: 171
End Page Number: 187
Publication Date: Apr 2010
Journal: Computational Management Science
Authors: , ,
Keywords: option pricing
Abstract:

This paper develops a new numerical technique to price an American option written upon an underlying asset that follows a bivariate diffusion process. The technique presented here exploits the supermartingale representation of an American option price together with a coarse approximation of its early exercise surface that is based on an efficient implementation of the least-squares Monte–Carlo algorithm (LSM) of Longstaff and Schwartz (2001). Our approach also has the advantage of avoiding two main issues associated with LSM, namely its inherent bias and the basis functions selection problem. Extensive numerical results show that our approach yields very accurate prices in a computationally efficient manner. Finally, the flexibility of our method allows for its extension to a much larger class of optimal stopping problems than addressed in this paper.

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