IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v16y2013i08ns0219024913500428.html
   My bibliography  Save this article

Automated Option Pricing: Numerical Methods

Author

Listed:
  • PIERRE HENRY-LABORDÈRE

    (Société Générale, Global Markets, Quantitative Research, 17 cours Valmy, La Défense, France)

Abstract

In this paper, we investigate model-independent bounds for option prices given a set of market instruments. This super-replication problem can be written as a semi-infinite linear programing problem. As these super-replication prices can be large and the densities ℚ which achieve the upper bounds quite singular, we restrict ℚ to be close in the entropy sense to a prior probability measure at a next stage. This leads to our risk-neutral weighted Monte Carlo approach which is connected to a constrained convex problem. We explain how to solve efficiently these large-scale problems using a primal-dual interior-point algorithm within the cutting-plane method and a quasi-Newton algorithm. Various examples illustrate the efficiency of these algorithms and the large range of applicability.

Suggested Citation

  • Pierre Henry-Labordère, 2013. "Automated Option Pricing: Numerical Methods," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(08), pages 1-27.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:08:n:s0219024913500428
    DOI: 10.1142/S0219024913500428
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024913500428
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024913500428?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1999. "Calibrating Volatility Surfaces Via Relative-Entropy Minimization," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 4, pages 121-151, World Scientific Publishing Co. Pte. Ltd..
    2. Pierre Henry-Labordere & Jan Obloj & Peter Spoida & Nizar Touzi, 2013. "Maximum Maximum of Martingales given Marginals," Working Papers hal-00684005, HAL.
    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


    Cited by:

    1. Pierre Henry-Labordère, 2019. "(Martingale) Optimal Transport And Anomaly Detection With Neural Networks: A Primal-Dual Algorithm," Working Papers hal-02095222, HAL.
    2. Julian Sester, 2023. "On intermediate Marginals in Martingale Optimal Transportation," Papers 2307.09710, arXiv.org, revised Nov 2023.
    3. Sester, Julian, 2024. "A multi-marginal c-convex duality theorem for martingale optimal transport," Statistics & Probability Letters, Elsevier, vol. 210(C).

    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. Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227, arXiv.org, revised Feb 2014.
    2. Dolinsky, Yan & Soner, H. Mete, 2015. "Martingale optimal transport in the Skorokhod space," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3893-3931.

    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:wsi:ijtafx:v:16:y:2013:i:08:n:s0219024913500428. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.