IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v35y2025i2p422-440.html
   My bibliography  Save this article

Tackling nonlinear price impact with linear strategies

Author

Listed:
  • Xavier Brokmann
  • David Itkin
  • Johannes Muhle‐Karbe
  • Peter Schmidt

Abstract

Empirical studies in various contexts find that the price impact of large trades approximately follows a power law with exponent between 0.4 and 0.7. Yet, tractable formulas for the portfolios that trade off predictive trading signals, risk, and trading costs in an optimal manner are only available for quadratic costs corresponding to linear price impact. In this paper, we show that the resulting linear strategies allow to achieve virtually optimal performance also for realistic nonlinear price impact, if the “effective” quadratic cost parameter is chosen appropriately. To wit, for a wide range of risk levels, this leads to performance losses below 2% compared to a numerical algorithm proposed by Kolm and Ritter, run at very high accuracy. The effective quadratic cost depends on the portfolio risk and concavity of the impact function, but can be computed without any sophisticated numerics by simply maximizing an explicit scalar function.

Suggested Citation

  • Xavier Brokmann & David Itkin & Johannes Muhle‐Karbe & Peter Schmidt, 2025. "Tackling nonlinear price impact with linear strategies," Mathematical Finance, Wiley Blackwell, vol. 35(2), pages 422-440, April.
    • Handle: RePEc:bla:mathfi:v:35:y:2025:i:2:p:422-440
    DOI: 10.1111/mafi.12449
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/mafi.12449
    Download Restriction: no
    File URL: https://libkey.io/10.1111/mafi.12449?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
    ---><---

    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:bla:mathfi:v:35:y:2025:i:2:p:422-440. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    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.