Advanced Search
MyIDEAS: Login to save this paper or follow this series

Maximum Maximum of Martingales given Marginals

Contents:

Author Info

  • Pierre Henry-Labordere

    (Société Générale - Société Générale)

  • Jan Obloj

    ()
    (MI - Mathematical Institute [Oxford] - University of Oxford)

  • Peter Spoida

    ()
    (MI - Mathematical Institute [Oxford] - University of Oxford)

  • Nizar Touzi

    ()
    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS : UMR7641)

Registered author(s):

    Abstract

    We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset and statically trade European call options for all possible strikes and finitely-many maturities. We present a general duality result which converts this problem into a min-max calculus of variations problem where the Lagrange multipliers correspond to the static part of the hedge. Following Galichon, Henry-Labordére and Touzi \cite{ght}, we apply stochastic control methods to solve it explicitly for Lookback options with a non-decreasing payoff function. The first step of our solution recovers the extended optimal properties of the Azéma-Yor solution of the Skorokhod embedding problem obtained by Hobson and Klimmek \cite{hobson-klimmek} (under slightly different conditions). The two marginal case corresponds to the work of Brown, Hobson and Rogers \cite{brownhobsonrogers}. The robust superhedging cost is complemented by (simple) dynamic trading and leads to a class of semi-static trading strategies. The superhedging property then reduces to a functional inequality which we verify independently. The optimality follows from existence of a model which achieves equality which is obtained in Ob\lój and Spoida \cite{OblSp}.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://hal.archives-ouvertes.fr/docs/00/80/94/05/PDF/host%207April2013.pdf
    Our checks indicate that this address may not be valid because: 404 Not Found (http://hal.archives-ouvertes.fr/docs/00/80/94/05/PDF/host%207April2013.pdf [302 Found]--> http://hal.archives-ouvertes.fr/err404.php). If this is indeed the case, please notify (CCSD)
    Download Restriction: no

    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00684005.

    as in new window
    Length:
    Date of creation: 07 Apr 2013
    Date of revision:
    Handle: RePEc:hal:wpaper:hal-00684005

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00684005
    Contact details of provider:
    Web page: http://hal.archives-ouvertes.fr/

    Related research

    Keywords: Optimal control; robust pricing and hedging; volatility uncertainty; optimal transportation; pathwise inequalities; lookback option.;

    This paper has been announced in the following NEP Reports:

    References

    References listed on IDEAS
    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.:
    as in new window
    1. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    2. Mathias Beiglb\"ock & Pierre Henry-Labord\`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
    3. 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 621-51, October.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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

    Cited by:
    1. Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227, arXiv.org, revised Feb 2014.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-00684005. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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