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Zbl 1213.91164
Salmi, Santtu; Toivanen, Jari
An iterative method for pricing American options under jump-diffusion models. (English)
[J] Appl. Numer. Math. 61, No. 7, 821-831 (2011). ISSN 0168-9274

Summary: We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting system to be dense. We propose an iteration to solve the LCPs efficiently and prove its convergence. Numerical examples with Kou's and Merton's jump-diffusion models show that the resulting iteration converges rapidly.

MSC 2000:: *91G60
65N06 Finite difference methods (BVP of PDE)
90C33 Complementarity problems
91G20

Keywords: American option; jump-diffusion model; finite difference method; linear complementarity problem; iterative method

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