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    A penalty-based method from reconstructing smooth local volatility surface from American options

    Access Status
    Open access via publisher
    Authors
    Zhang, K.
    Teo, Kok Lay
    Date
    2015
    Type
    Journal Article
    
    Metadata
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    Citation
    Zhang, K. and Teo, K.L. 2015. A penalty-based method from reconstructing smooth local volatility surface from American options. Journal of Industrial and Management Optimization (JIMO). 11 (2): pp. 631-644.
    Source Title
    Journal of Industrial and Management Optimization (JIMO)
    DOI
    10.3934/jimo.2015.11.631
    ISSN
    1553-166X
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/3463
    Collection
    • Curtin Research Publications
    Abstract

    This paper is devoted to develop a robust penalty-based method of reconstructing smooth local volatility surface from the observed American option prices. This reconstruction problem is posed as an inverse problem: given a nite set of observed American option prices, nd a local volatility function such that the theoretical option prices matches the observed ones optimally with respect to a prescribed performance criterion. The theoretical American option prices are governed by a set of partial dierential complementarity problems (PDCP). We propose a penalty-based numerical method for the solution of the PDCP. Typically, the reconstruction problem is ill-posed and a bicubic spline regularization technique is thus proposed to overcome this diculty. We apply a gradient-based optimization algorithm to solve this nonlinear optimization problem, where the Jacobian of the cost function is computed via nite dierence approximation. Two numerical experiments: a synthetic American put option example and a real market American put option example, are performed to show the robustness and eectiveness of the proposed method to reconstructing the unknown volatility surface.

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