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Meshfree Approximation for Multi-Asset Options

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Author Info

  • Emmanuel Hanert

    (Départment des sciences du milieu et de l'aménagement du territoire, Université catholique de Louvain)

  • Aanand Venkatramanan

    ()
    (ICMA Centre, University of Reading)

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    Abstract

    We price multi-asset options by solving their price partial differential equations using a meshfree approach with radial basis functions under jump-diffusion and geometric Brownian motion frameworks. In the geometric Brownian motion framework, we propose an effective technique that breaks the multi-dimensional problem to multiple 3D problems. We solve the price PDEs or PIDEs with an implicit meshfree scheme using thin-plate radial basis functions. Meshfree approach is very accurate, has high order of convergence and is easily scalable and adaptable to higher dimensions and different payoff profiles. We also obtain closed form approximations for the option Greeks. We test the model on American crack spread options traded on NYMEX.

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    File URL: http://www.icmacentre.ac.uk/files/meshfree_approximation_for_multiasset_options.pdf
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    Bibliographic Info

    Paper provided by Henley Business School, Reading University in its series ICMA Centre Discussion Papers in Finance with number icma-dp2009-07.

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    Length: 22 pages
    Date of creation: Jul 2008
    Date of revision: Jun 2009
    Handle: RePEc:rdg:icmadp:icma-dp2009-07

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    Phone: +44 (0) 118 378 8226
    Fax: +44 (0) 118 975 0236
    Web page: http://www.henley.reading.ac.uk/
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    Related research

    Keywords: Multi-asset options; radial basis function; meshfree approximation; collocation; multidimensional Lévy process; basket options; PIDE; PDE;

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    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Carol Alexander & Aanand Venkatramanan, 2007. "Analytic Approximations for Spread Options," ICMA Centre Discussion Papers in Finance icma-dp2007-11, Henley Business School, Reading University.
    2. Szymon Borak & Kai Detlefsen & Wolfgang Härdle, 2005. "FFT Based Option Pricing," SFB 649 Discussion Papers SFB649DP2005-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Carol Alexander & Aanand Venkatramanan, 2008. "Analytic Approximations for Multi-Asset Option Pricing," ICMA Centre Discussion Papers in Finance icma-dp2009-05, Henley Business School, Reading University, revised Jun 2009.
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