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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 236091, 8 pages
http://dx.doi.org/10.1155/2014/236091
Research Article

Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market

1Department of Maths and Statistics, Curtin University, Perth, WA 6845, Australia
2School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
3School of Finance, Zhongnan University of Economics and Law, Wuhan 430073, China
4Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand

Received 29 December 2013; Accepted 17 January 2014; Published 26 February 2014

Academic Editor: Yonghong Wu

Copyright © 2014 Shuang Li et al. 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 pricing of American options in an incomplete market in which the dynamics of the underlying risky asset is driven by a jump diffusion process with stochastic volatility. By employing a risk-minimization criterion, we obtain the Radon-Nikodym derivative for the minimal martingale measure and consequently a linear complementarity problem (LCP) for American option price. An iterative method is then established to solve the LCP problem for American put option price. Our numerical results show that the model and numerical scheme are robust in capturing the feature of incomplete finance market, particularly the influence of market volatility on the price of American options.