Efficient pricing of commodity options with early-exercise under the Ornstein-Uhlenbeck process

Authors:
B. Zhang;L. A. Grzelak;C. W. Oosterlee
Affiliations:
Delft University of Technology, Mekelweg 4, 2628CD, Delft, The Netherlands;Delft University of Technology, Mekelweg 4, 2628CD, Delft, The Netherlands and Rabobank International, Utrecht, The Netherlands;Delft University of Technology, Mekelweg 4, 2628CD, Delft, The Netherlands and CWI - Centrum Wiskunde & Informatica, Amsterdam, The Netherlands
Venue:
Applied Numerical Mathematics
Year:
2012

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Abstract

We analyze the efficiency properties of a numerical pricing method based on Fourier-cosine expansions for early-exercise options. We focus on variants of Schwartz@? model based on a mean reverting Ornstein-Uhlenbeck process, which is commonly used for modeling commodity prices. This process however does not possess favorable properties for the option pricing method of interest. We therefore propose an approximation of its characteristic function, so that the Fast Fourier Transform can be applied for highest efficiency.