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

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


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