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Model-independent bounds for option prices—a mass transport approach

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  • Mathias Beiglböck

    ()

  • Pierre Henry-Labordère

    ()

  • Friedrich Penkner

    ()

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    Abstract

    In this paper we investigate model-independent bounds for exotic options written on a risky asset using infinite-dimensional linear programming methods. 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. Copyright Springer-Verlag Berlin Heidelberg 2013

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    File URL: http://hdl.handle.net/10.1007/s00780-013-0205-8
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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 17 (2013)
    Issue (Month): 3 (July)
    Pages: 477-501

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    Handle: RePEc:spr:finsto:v:17:y:2013:i:3:p:477-501

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    Related research

    Keywords: Model-independent pricing; Monge–Kantorovich transport problem; Option arbitrage; Robust superreplication theorem; 91G20; 91G80; C61; G13;

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    References

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    1. H. Albrecher & P. A. Mayer & W. Schoutens, 2008. "General Lower Bounds for Arithmetic Asian Option Prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 123-149.
    2. Alexander Cox & Jan Obłój, 2011. "Robust pricing and hedging of double no-touch options," Finance and Stochastics, Springer, vol. 15(3), pages 573-605, September.
    3. Cousot, Laurent, 2007. "Conditions on option prices for absence of arbitrage and exact calibration," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3377-3397, November.
    4. 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.
    5. 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.
    6. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    7. Peter Carr & Roger Lee, 2010. "Hedging variance options on continuous semimartingales," Finance and Stochastics, Springer, vol. 14(2), pages 179-207, April.
    8. 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.
    9. David Hobson & Martin Klimmek, 2012. "Model-independent hedging strategies for variance swaps," Finance and Stochastics, Springer, vol. 16(4), pages 611-649, October.
    10. Peter Laurence & Tai-Ho Wang, 2005. "Sharp Upper and Lower Bounds for Basket Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(3), pages 253-282.
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    Cited by:
    1. Yan Dolinsky & H. Soner, 2014. "Robust hedging with proportional transaction costs," Finance and Stochastics, Springer, vol. 18(2), pages 327-347, April.
    2. Alexander M. G. Cox & Zhaoxu Hou & Jan Obloj, 2014. "Robust pricing and hedging under trading restrictions and the emergence of local martingale models," Papers 1406.0551, arXiv.org.
    3. Mathias Beiglb\"ock & Marcel Nutz, 2014. "Martingale Inequalities and Deterministic Counterparts," Papers 1401.4698, arXiv.org.
    4. Erhan Bayraktar & Yu-Jui Huang & Zhou Zhou, 2013. "On hedging American options under model uncertainty," Papers 1309.2982, arXiv.org, revised Feb 2014.
    5. Y. Dolinsky & H. M. Soner, 2014. "Martingale optimal transport in the Skorokhod space," Papers 1404.1516, arXiv.org.
    6. Nicolas Perkowski & David J. Pr\"omel, 2013. "Pathwise stochastic integrals for model free finance," Papers 1311.6187, arXiv.org.
    7. Alexander M. G. Cox & Jiajie Wang, 2013. "Optimal robust bounds for variance options," Papers 1308.4363, arXiv.org.
    8. Arash Fahim & Yu-Jui Huang, 2014. "Model-independent Superhedging under Portfolio Constraints," Papers 1402.2599, arXiv.org.
    9. Luciano Campi & Ismail Laachir & Claude Martini, 2014. "Change of numeraire in the two-marginals martingale transport problem," Papers 1406.6951, arXiv.org, revised Jun 2014.

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