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    A finite difference method for pricing European and American options under a geometric Lévy process

    231825_231825.pdf (1.046Mb)
    Access Status
    Open access
    Authors
    Chen, W.
    Wang, Song
    Date
    2015
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Chen, W. and Wang, S. 2015. A finite difference method for pricing European and American options under a geometric Lévy process. Journal of Industrial and Management Optimization. 11 (1): pp. 241-264.
    Source Title
    Journal of Industrial and Management Optimization
    DOI
    10.3934/jimo.2015.11.241
    ISSN
    1547-5816
    School
    Department of Mathematics and Statistics
    Remarks

    This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Industrial and Management Optimization following peer review. The definitive publisher-authenticated version Chen, W. and Wang, S. 2015. A finite difference method for pricing European and American options under a geometric Lévy process. Journal of Industrial and Management Optimization. 11 (1): pp. 241-264 is available online at: http://doi.org/10.3934/jimo.2015.11.241

    URI
    http://hdl.handle.net/20.500.11937/40837
    Collection
    • Curtin Research Publications
    Abstract

    In this paper we develop a numerical approach to a fractional-order differential Linear Complementarity Problem (LCP) arising in pricing European and American options under a geometric Lévy process. The LCP is first approximated by a nonlinear penalty fractional Black-Scholes (fBS) equation. We then propose a finite difference scheme for the penalty fBS equation. We show that both the continuous and the discretized fBS equations are uniquely solvable and establish the convergence of the numerical solution to the viscosity solution of the penalty fBS equation by proving the consistency, stability and monotonicity of the numerical scheme. We also show that the discretization has the 2nd-order truncation error in both the spatial and time mesh sizes. Numerical results are presented to demonstrate the accuracy and usefulness of the numerical method for pricing both European and American options under the geometric Lévy process.

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