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October  2008, 4(4): 783-799. doi: 10.3934/jimo.2008.4.783

A power penalty approach to american option pricing with jump diffusion processes

Kai Zhang 1, , Xiaoqi Yang 2, and  Kok Lay Teo 3,

1. 

Department of Finance, Business School, Shenzhen University, Nanhai Ave 3688, Shenzhen, Guangdong 518060, China
2. 

Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong
3. 

Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845

Received  February 2008 Revised  August 2008 Published  November 2008

This paper is devoted to develop a power penalty method for pricing the American option model where the underlying asset is assumed to follow a jump diffusion process. With the help of the linear complementarity problem and variational inequalities, we propose a power penalty approach for a partial integro-differential complementarity problem, which is the mathematical model of pricing the American option with a jump diffusion process. The convergence analysis of the power penalty approach is established. Finally, based on the finite element discretization, a numerical scheme is developed to solve the penalized problem and the numerical tests are designed to illustrate the efficiency of this method.
Keywords: American option pricing, finite element method., penalty method.
Mathematics Subject Classification: Primary: 91B28; Secondary: 35K20, 90C3.
Citation: Kai Zhang, Xiaoqi Yang, Kok Lay Teo. A power penalty approach to american option pricing with jump diffusion processes. Journal of Industrial and Management Optimization, 2008, 4 (4) : 783-799. doi: 10.3934/jimo.2008.4.783
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