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Model-independent Bounds for Option Prices: A Mass Transport Approach

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  • Mathias Beiglb\"ock
  • Pierre Henry-Labord\`ere
  • Friedrich Penkner
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    Abstract

    In this paper we investigate model-independent bounds for exotic options written on a risky asset. Based on arguments from the theory of Monge-Kantorovich mass-transport we establish a dual version of the problem that has a natural financial interpretation in terms of semi-static hedging. In particular we prove that there is no duality gap.

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    File URL: http://arxiv.org/pdf/1106.5929
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1106.5929.

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    Date of creation: Jun 2011
    Date of revision: Feb 2013
    Handle: RePEc:arx:papers:1106.5929

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    Web page: http://arxiv.org/

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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. Hobson, David & Laurence, Peter & Wang, Tai-Ho, 2005. "Static-arbitrage optimal subreplicating strategies for basket options," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 553-572, December.
    2. Chen, X. & Deelstra, G. & Dhaene, J. & Vanmaele, M., 2008. "Static super-replicating strategies for a class of exotic options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1067-1085, June.
    3. David Hobson & Peter Laurence & Tai-Ho Wang, 2005. "Static-arbitrage upper bounds for the prices of basket options," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 329-342.
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    Cited by:
    1. Mathias Beiglb\"ock & Marcel Nutz, 2014. "Martingale Inequalities and Deterministic Counterparts," Papers 1401.4698, arXiv.org.
    2. Pierre Henry-Labordere & Jan Obloj & Peter Spoida & Nizar Touzi, 2013. "Maximum Maximum of Martingales given Marginals," Working Papers hal-00684005, HAL.
    3. Arash Fahim & Yu-Jui Huang, 2014. "Model-independent Superhedging under Portfolio Constraints," Papers 1402.2599, arXiv.org.
    4. Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227, arXiv.org, revised Feb 2014.
    5. Pierre Henry-Labordere & Jan Obloj & Peter Spoida & Nizar Touzi, 2012. "Maximum Maximum of Martingales given Marginals," Papers 1203.6877, arXiv.org, revised Apr 2013.
    6. Erhan Bayraktar & Yu-Jui Huang & Zhou Zhou, 2013. "On hedging American options under model uncertainty," Papers 1309.2982, arXiv.org, revised Feb 2014.
    7. Erhan Bayraktar & Zhou Zhou, 2013. "On model-independent pricing/hedging using shortfall risk and quantiles," Papers 1307.2493, arXiv.org.
    8. Alexander M. G. Cox & Jiajie Wang, 2013. "Optimal robust bounds for variance options," Papers 1308.4363, arXiv.org.
    9. Nicolas Perkowski & David J. Pr\"omel, 2013. "Pathwise stochastic integrals for model free finance," Papers 1311.6187, arXiv.org.

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