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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 651573, 11 pages
http://dx.doi.org/10.1155/2013/651573
Research Article

A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model

Institute of Mathematics, Zhejiang Wanli University, Ningbo, Zhejiang 315100, China

Received 30 September 2012; Revised 15 December 2012; Accepted 17 December 2012

Academic Editor: M. Ruiz Galan

Copyright © 2013 Jian Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a stable finite difference scheme on a piecewise uniform mesh along with a penalty method for pricing American put options under Kou's jump-diffusion model. By adding a penalty term, the partial integrodifferential complementarity problem arising from pricing American put options under Kou's jump-diffusion model is transformed into a nonlinear parabolic integro-differential equation. Then a finite difference scheme is proposed to solve the penalized integrodifferential equation, which combines a central difference scheme on a piecewise uniform mesh with respect to the spatial variable with an implicit-explicit time stepping technique. This leads to the solution of problems with a tridiagonal M-matrix. It is proved that the difference scheme satisfies the early exercise constraint. Furthermore, it is proved that the scheme is oscillation-free and is second-order convergent with respect to the spatial variable. The numerical results support the theoretical results.