Journal of Probability and Statistics
Volume 2010 (2010), Article ID 863585, 18 pages
doi:10.1155/2010/863585
Research Article

Viscosity Solutions and American Option Pricing in a Stochastic Volatility Model of the Ornstein-Uhlenbeck Type

Alexandre F. Roch

Departement Mathematik, ETH Zürich, 8092 Zürich, Switzerland

Received 4 January 2010; Revised 14 June 2010; Accepted 6 July 2010

Academic Editor: Junbin B. Gao

Copyright © 2010 Alexandre F. Roch. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the valuation of American-type derivatives in the stochastic volatility model of Barndorff-Nielsen and Shephard (2001). We characterize the value of such derivatives as the unique viscosity solution of an integral-partial differential equation when the payoff function satisfies a Lipschitz condition.