IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1503.02822.html
   My bibliography  Save this paper

On robust pricing-hedging duality in continuous time

Author

Listed:
  • Zhaoxu Hou
  • Jan Obloj

Abstract

We pursue robust approach to pricing and hedging in mathematical finance. We consider a continuous time setting in which some underlying assets and options, with continuous paths, are available for dynamic trading and a further set of European options, possibly with varying maturities, is available for static trading. Motivated by the notion of prediction set in Mykland (2003), we include in our setup modelling beliefs by allowing to specify a set of paths to be considered, e.g. super-replication of a contingent claim is required only for paths falling in the given set. Our framework thus interpolates between model-independent and model-specific settings and allows to quantify the impact of making assumptions or gaining information. We obtain a general pricing-hedging duality result: the infimum over superhedging prices is equal to supremum over calibrated martingale measures. In presence of non-trivial beliefs, the equality is between limiting values of perturbed problems. In particular, our results include the martingale optimal transport duality of Dolinsky and Soner (2013) and extend it to multiple dimensions and multiple maturities.

Suggested Citation

  • Zhaoxu Hou & Jan Obloj, 2015. "On robust pricing-hedging duality in continuous time," Papers 1503.02822, arXiv.org, revised Jul 2015.
    • Handle: RePEc:arx:papers:1503.02822
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1503.02822
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2013. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
    2. Jan Obłój & Frédérik Ulmer, 2012. "Performance Of Robust Hedges For Digital Double Barrier Options," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 23, pages 521-554, World Scientific Publishing Co. Pte. Ltd..
    3. Erhan Bayraktar & Zhou Zhou, 2017. "On Arbitrage And Duality Under Model Uncertainty And Portfolio Constraints," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 988-1012, October.
    4. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    5. Jan Obłój & Frédérik Ulmer, 2012. "Performance Of Robust Hedges For Digital Double Barrier Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-34.
    6. Arash Fahim & Yu-Jui Huang, 2014. "Model-independent Superhedging under Portfolio Constraints," Papers 1402.2599, arXiv.org, revised Jun 2015.
    7. Gianluca Cassese, 2008. "Asset Pricing With No Exogenous Probability Measure," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 23-54, January.
    8. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2014. "Universal Arbitrage Aggregator in Discrete Time Markets under Uncertainty," Papers 1407.0948, arXiv.org, revised Feb 2015.
    9. 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.
    10. Beatrice Acciaio & Mathias Beiglbock & Friedrich Penkner & Walter Schachermayer, 2013. "A model-free version of the fundamental theorem of asset pricing and the super-replication theorem," Papers 1301.5568, arXiv.org, revised Mar 2013.
    11. Walter Schachermayer, 2013. "The Fundamental Theorem of Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 2, pages 31-48, World Scientific Publishing Co. Pte. Ltd..
    12. T. J. Lyons, 1995. "Uncertain volatility and the risk-free synthesis of derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 117-133.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhaoxu Hou & Jan Obłój, 2018. "Robust pricing–hedging dualities in continuous time," Finance and Stochastics, Springer, vol. 22(3), pages 511-567, July.
    2. Sergey Nadtochiy & Jan Obłój, 2017. "Robust Trading Of Implied Skew," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-41, March.
    3. Beatrice Acciaio & Martin Larsson, 2015. "Semi-static completeness and robust pricing by informed investors," Papers 1510.01890, arXiv.org, revised Sep 2016.
    4. Sergey Nadtochiy & Jan Obloj, 2016. "Robust Trading of Implied Skew," Papers 1611.05518, arXiv.org.
    5. Sebastian Herrmann & Johannes Muhle-Karbe, 2017. "Model uncertainty, recalibration, and the emergence of delta–vega hedging," Finance and Stochastics, Springer, vol. 21(4), pages 873-930, October.
    6. Sebastian Herrmann & Johannes Muhle-Karbe, 2017. "Model Uncertainty, Recalibration, and the Emergence of Delta-Vega Hedging," Papers 1704.04524, arXiv.org.
    7. 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, revised Jun 2015.
    8. Sergey Badikov & Mark H. A. Davis & Antoine Jacquier, 2018. "Perturbation analysis of sub/super hedging problems," Papers 1806.03543, arXiv.org, revised May 2021.
    9. Matteo Burzoni & Marco Frittelli & Marco Maggis, 2015. "Model-free Superhedging Duality," Papers 1506.06608, arXiv.org, revised May 2016.
    10. Erhan Bayraktar & Yu-Jui Huang & Zhou Zhou, 2013. "On hedging American options under model uncertainty," Papers 1309.2982, arXiv.org, revised Apr 2015.
    11. Acciaio, Beatrice & Larsson, Martin, 2017. "Semi-static completeness and robust pricing by informed investors," LSE Research Online Documents on Economics 68502, London School of Economics and Political Science, LSE Library.
    12. Sara Biagini & Bruno Bouchard & Constantinos Kardaras & Marcel Nutz, 2014. "Robust Fundamental Theorem for Continuous Processes," Papers 1410.4962, arXiv.org, revised Jul 2015.
    13. David Hobson & Martin Klimmek, 2013. "Robust price bounds for the forward starting straddle," Papers 1304.2141, arXiv.org.
    14. 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.
    15. Wiesel Johannes & Zhang Erica, 2023. "An optimal transport-based characterization of convex order," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-15, January.
    16. Daniel Bartl & Michael Kupper & David J. Prömel & Ludovic Tangpi, 2019. "Duality for pathwise superhedging in continuous time," Finance and Stochastics, Springer, vol. 23(3), pages 697-728, July.
    17. Alessandro Doldi & Marco Frittelli, 2023. "Entropy martingale optimal transport and nonlinear pricing–hedging duality," Finance and Stochastics, Springer, vol. 27(2), pages 255-304, April.
    18. Nutz, Marcel, 2015. "Robust superhedging with jumps and diffusion," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4543-4555.
    19. Patrick Cheridito & Michael Kupper & Ludovic Tangpi, 2016. "Duality formulas for robust pricing and hedging in discrete time," Papers 1602.06177, arXiv.org, revised Sep 2017.
    20. David Hobson & Dominykas Norgilas, 2019. "Robust bounds for the American put," Finance and Stochastics, Springer, vol. 23(2), pages 359-395, April.

    More about this item

    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:arx:papers:1503.02822. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.