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Meshfree Approximation for Multi-Asset Options

Author

Listed:
  • Emmanuel Hanert

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

  • Aanand Venkatramanan

    (ICMA Centre, University of Reading)

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.

Suggested Citation

  • Emmanuel Hanert & Aanand Venkatramanan, 2008. "Meshfree Approximation for Multi-Asset Options," ICMA Centre Discussion Papers in Finance icma-dp2009-07, Henley Business School, University of Reading, revised Jun 2009.
    • Handle: RePEc:rdg:icmadp:icma-dp2009-07
    as

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    File URL: http://www.icmacentre.ac.uk/files/meshfree_approximation_for_multiasset_options.pdf
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    References listed on IDEAS

    as
    1. Carol Alexander & Aanand Venkatramanan, 2007. "Analytic Approximations for Spread Options," ICMA Centre Discussion Papers in Finance icma-dp2007-11, Henley Business School, University of Reading.
    2. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    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, University of Reading, revised Jun 2009.
    4. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
    5. Borak, Szymon & Detlefsen, Kai & Härdle, Wolfgang Karl, 2005. "FFT based option pricing," SFB 649 Discussion Papers 2005-011, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

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    More about this item

    Keywords

    Multi-asset options; radial basis function; meshfree approximation; collocation; multidimensional Lévy process; basket options; PIDE; PDE;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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