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A model-free no-arbitrage price bound for variance options

  • J. Frederic Bonnans

    ()

    (INRIA Saclay - Ile de France - COMMANDS - INRIA - CNRS : UMR7641 - Polytechnique - X - ENSTA ParisTech, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS : UMR7641)

  • Xiaolu Tan

    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS : UMR7641)

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    In the framework of Galichon, Henry-Labordère and Touzi, we consider the model-free no-arbitrage bound of variance option given the marginal distributions of the underlying asset. We first make some approximations which restrict the computation on a bounded domain. Then we propose a gradient projection algorithm together with a finite difference scheme to approximate the bound. The general convergence result is obtained. We also provide a numerical example on the variance swap option.

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    File URL: http://hal.inria.fr/docs/00/63/43/87/PDF/RR-7777.pdf
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    Paper provided by HAL in its series Post-Print with number inria-00634387.

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    Date of creation: 04 Jul 2013
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    Publication status: Published, Applied Mathematics and Optimization, 2013, 68, 1, 43-73
    Handle: RePEc:hal:journl:inria-00634387
    Note: View the original document on HAL open archive server: http://hal.inria.fr/inria-00634387
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    1. Peter Carr & Roger Lee, 2010. "Hedging variance options on continuous semimartingales," Finance and Stochastics, Springer, vol. 14(2), pages 179-207, April.
    2. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
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