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    A numerical scheme for pricing american options with transaction costs under a jump diffusion process

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    Authors
    Lesmana, D.
    Wang, Song
    Date
    2017
    Type
    Journal Article
    
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    Citation
    Lesmana, D. and Wang, S. 2017. A numerical scheme for pricing american options with transaction costs under a jump diffusion process. Journal of Industrial and management optimization. 13 (4): pp. 1793-1813.
    Source Title
    Journal of Industrial and management optimization
    DOI
    10.3934/jimo.2017019
    ISSN
    1547-5816
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/58032
    Collection
    • Curtin Research Publications
    Abstract

    In this paper we develop a numerical method for a nonlinear partial integro-differential complementarity problem arising from pricing American options with transaction costs when the underlying assets follow a jump diffusion process. We first approximate the complementarity problem by a nonlinear partial integro-differential equation (PIDE) using a penalty approach. The PIDE is then discretized by a combination of a spatial upwind finite differencing and a fully implicit time stepping scheme. We prove that the coeficient matrix of the system from this scheme is an M-matrix and that the approximate solution converges to the viscosity solution to the PIDE by showing that the scheme is consistent, monotone, and unconditionally stable. We also propose a Newton's iterative method coupled with a Fast Fourier Transform for the computation of the discretized integral term for solving the fully discretized system. Numerical results will be presented to demonstrate the convergence rates and usefulness of this method.

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