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An iterative method for pricing American options under jump-diffusion models. (English) Zbl 1213.91164
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:
91G60 Numerical methods (including Monte Carlo methods)
65N06 Finite difference methods for boundary value problems involving PDEs
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
91G20 Derivative securities (option pricing, hedging, etc.)
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