An iterative method for pricing American options under jump-diffusion models

Authors:
Santtu Salmi;Jari Toivanen
Affiliations:
Department of Mathematical Information Technology, P.O. Box 35 (Agora), FI-40014 University of Jyväskylä, Finland;Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA and Department of Mathematical Information Technology, P.O. Box 35 (Agora), FI-40014 Universi ...
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

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.