IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v17y2014i07ns0219024914500423.html
   My bibliography  Save this article

Estimating Residual Hedging Risk With Least-Squares Monte Carlo

Author

Listed:
  • STEFAN ANKIRCHNER

    (Institute for Mathematics, University of Jena, 07743 Jena, Ernst-Abbe-Platz 2, Germany)

  • CHRISTIAN PIGORSCH

    (Faculty of Economics and Business Administration, University of Jena, 07743 Jena, Carl-Zeiß-Straße 3, Germany)

  • NIKOLAUS SCHWEIZER

    (Mercator School of Management, University of Duisburg-Essen, 47057 Duisburg, Lotharstraße 65, Germany)

Abstract

Frequently, dynamic hedging strategies minimizing risk exposure are not given in closed form, but need to be approximated numerically. This makes it difficult to estimate residual hedging risk, also called basis risk, when only imperfect hedging instruments are at hand. We propose an easy to implement and computationally efficient least-squares Monte Carlo algorithm to estimate residual hedging risk. The algorithm approximates the variance minimal hedging strategy within general diffusion models. Moreover, the algorithm produces both high-biased and low-biased estimators for the residual hedging error variance, thus providing an intrinsic criterion for the quality of the approximation. In a number of examples we show that the algorithm delivers accurate hedging error characteristics within seconds.

Suggested Citation

  • Stefan Ankirchner & Christian Pigorsch & Nikolaus Schweizer, 2014. "Estimating Residual Hedging Risk With Least-Squares Monte Carlo," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 1-29.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:07:n:s0219024914500423
    DOI: 10.1142/S0219024914500423
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024914500423
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024914500423?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. Hardy Hulley & Thomas A. McWalter, 2015. "Quadratic Hedging of Basis Risk," JRFM, MDPI, vol. 8(1), pages 1-20, February.
    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. Ankirchner, Stefan & Dimitroff, Georgi & Heyne, Gregor & Pigorsch, Christian, 2012. "Futures Cross-Hedging with a Stationary Basis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(6), pages 1361-1395, December.
    2. Michael Monoyios, 2010. "Utility-Based Valuation and Hedging of Basis Risk With Partial Information," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 519-551.
    3. Ismail Laachir & Francesco Russo, 2016. "BSDEs, càdlàg martingale problems and orthogonalisation under basis risk," Working Papers hal-01086227, HAL.
    4. Ismail Laachir & Francesco Russo, 2016. "BSDEs, càdlàg martingale problems and orthogonalisation under basis risk," Post-Print hal-01086227, HAL.
    5. Bauer Jan, 2020. "Hedging of Variable Annuities under Basis Risk," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(2), pages 1-34, July.
    6. Stefan Ankirchner & Gregor Heyne, 2012. "Cross hedging with stochastic correlation," Finance and Stochastics, Springer, vol. 16(1), pages 17-43, January.

    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:17:y:2014:i:07:n:s0219024914500423. 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.