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


  • J. Frederic Bonnans

    () (Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems - CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique - UMA - Unité de Mathématiques Appliquées - Univ. Paris-Saclay, ENSTA ParisTech - École Nationale Supérieure de Techniques Avancées - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique, CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Xiaolu Tan

    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)


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.

Suggested Citation

  • J. Frederic Bonnans & Xiaolu Tan, 2013. "A model-free no-arbitrage price bound for variance options," Post-Print inria-00634387, HAL.
  • Handle: RePEc:hal:journl:inria-00634387
    DOI: 10.1007/s00245-013-9197-1
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    References listed on IDEAS

    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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    Cited by:

    1. Henry-Labordère, Pierre & Tan, Xiaolu & Touzi, Nizar, 2016. "An explicit martingale version of the one-dimensional Brenier’s Theorem with full marginals constraint," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2800-2834.
    2. Erhan Bayraktar & Christopher W. Miller, 2016. "Distribution-Constrained Optimal Stopping," Papers 1604.03042,, revised Jul 2017.
    3. Sebastian Herrmann & Florian Stebegg, 2017. "Robust Pricing and Hedging around the Globe," Papers 1707.08545,
    4. Christopher W. Miller, 2016. "A Duality Result for Robust Optimization with Expectation Constraints," Papers 1610.01227,
    5. Gaoyue Guo & Jan Obloj, 2017. "Computational Methods for Martingale Optimal Transport problems," Papers 1710.07911,
    6. Gaoyue Guo & Xiaolu Tan & Nizar Touzi, 2015. "Optimal Skorokhod embedding under finitely-many marginal constraints," Papers 1506.04063,, revised Aug 2016.

    More about this item


    gradient projection algorithm; Variance option; model-free price bound; gradient projection algorithm.;

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