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

Kai Zhang; Xiaoqi Yang; Kok Lay Teo

doi:10.3934/jimo.2008.4.783

Article Contents

2008, Volume 4, Issue 4: 783-799. Doi: 10.3934/jimo.2008.4.783

This issue Previous Article Sequential characterization of solutions in convex composite programming and applications to vector optimization Next Article On maximizing the expected terminal utility by investment and reinsurance

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

1.
Department of Finance, Business School, Shenzhen University, Nanhai Ave 3688, Shenzhen, Guangdong 518060
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: January 31, 2008

Revised: July 31, 2008

Published: September 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 91B28; Secondary: 35K20, 90C33.

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