IDEAS home Printed from https://ideas.repec.org/p/chf/rpseri/rp1313.html
   My bibliography  Save this paper

Martingale Optimal Transport and Robust Hedging in Continuous Time

Author

Listed:
  • Yan Dolinsky

    (ETH Zürich)

  • Halil Mete Soner

    (ETH Zürich; Swiss Finance Institute)

Abstract

The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging problem is to construct a minimal super-hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given, fi xed maturity. The dual is a Monge-Kantorovich type martingale transport problem of maximizing the expected value of the option over all martingale measures that has the given marginal at maturity. In addition to duality, a family of simple, piecewise constant super-replication portfolios that asymptotically achieve the minimal super-replication cost is constructed.

Suggested Citation

  • Yan Dolinsky & Halil Mete Soner, 2013. "Martingale Optimal Transport and Robust Hedging in Continuous Time," Swiss Finance Institute Research Paper Series 13-13, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1313
    as

    Download full text from publisher

    File URL: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2245481
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Erhan Bayraktar & Zhou Zhou, 2013. "On model-independent pricing/hedging using shortfall risk and quantiles," Papers 1307.2493, arXiv.org.
    2. Miklós Rásonyi & Andrea Meireles‐Rodrigues, 2021. "On utility maximization under model uncertainty in discrete‐time markets," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 149-175, January.
    3. Alexander M. G. Cox & Jiajie Wang, 2013. "Optimal robust bounds for variance options," Papers 1308.4363, arXiv.org.
    4. Erhan Bayraktar & Yu-Jui Huang & Zhou Zhou, 2013. "On hedging American options under model uncertainty," Papers 1309.2982, arXiv.org, revised Apr 2015.
    5. Yan Dolinsky & H. Mete Soner, 2017. "Convex Duality with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 42(2), pages 448-471, May.
    6. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2015. "Model-free Superhedging Duality," Papers 1506.06608, arXiv.org, revised May 2016.
    7. Arash Fahim & Yu-Jui Huang, 2014. "Model-independent Superhedging under Portfolio Constraints," Papers 1402.2599, arXiv.org, revised Jun 2015.
    8. David Hobson & Martin Klimmek, 2013. "Robust price bounds for the forward starting straddle," Papers 1304.2141, arXiv.org.
    9. Alexander M. G. Cox & Sigrid Kallblad, 2015. "Model-independent bounds for Asian options: a dynamic programming approach," Papers 1507.02651, arXiv.org, revised Jul 2016.
    10. Zhaoxu Hou & Jan Obloj, 2015. "On robust pricing-hedging duality in continuous time," Papers 1503.02822, arXiv.org, revised Jul 2015.
    11. Yan Dolinsky & H. Mete Soner, 2015. "Convex duality with transaction costs," Papers 1502.01735, arXiv.org, revised Oct 2015.

    More about this item

    Keywords

    European Options; Robust Hedging; Min-Max Theorems; Prokhorov Metric; Optimal transport;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:chf:rpseri:rp1313. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ridima Mittal (email available below). General contact details of provider: https://edirc.repec.org/data/fameech.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.