×

A power penalty approach to American option pricing with jump diffusion processes. (English) Zbl 1157.91378

Summary: 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.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60G40 Stopping times; optimal stopping problems; gambling theory
35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
35R60 PDEs with randomness, stochastic partial differential equations
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
91G60 Numerical methods (including Monte Carlo methods)
PDFBibTeX XMLCite
Full Text: DOI