IDEAS home Printed from https://ideas.repec.org/a/taf/apmtfi/v28y2021i2p101-142.html
   My bibliography  Save this article

Closed-form Approximations in Multi-asset Market Making

Author

Listed:
  • Philippe Bergault
  • David Evangelista
  • Olivier Guéant
  • Douglas Vieira

Abstract

A large proportion of market making models derive from the seminal model of Avellaneda and Stoikov. The numerical approximation of the value function and the optimal quotes in these models remains a challenge when the number of assets is large. In this article, we propose closed-form approximations for the value functions of many multi-asset extensions of the Avellaneda–Stoikov model. These approximations or proxies can be used (i) as heuristic evaluation functions, (ii) as initial value functions in reinforcement learning algorithms, and/or (iii) directly to design quoting strategies through a greedy approach. Regarding the latter, our results lead to new and easily interpretable closed-form approximations for the optimal quotes, both in the finite-horizon case and in the asymptotic (ergodic) regime.

Suggested Citation

  • Philippe Bergault & David Evangelista & Olivier Guéant & Douglas Vieira, 2021. "Closed-form Approximations in Multi-asset Market Making," Applied Mathematical Finance, Taylor & Francis Journals, vol. 28(2), pages 101-142, March.
    • Handle: RePEc:taf:apmtfi:v:28:y:2021:i:2:p:101-142
    DOI: 10.1080/1350486X.2021.1949359
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/1350486X.2021.1949359
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/1350486X.2021.1949359?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    Citations

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


    Cited by:

    1. Vincent Ragel & Damien Challet, 2024. "Consistent time travel for realistic interactions with historical data: reinforcement learning for market making," Papers 2408.02322, arXiv.org, revised Jan 2025.
    2. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant & Julien Guilbert, 2024. "Price-Aware Automated Market Makers: Models Beyond Brownian Prices and Static Liquidity," Papers 2405.03496, arXiv.org, revised May 2024.
    3. Bastien Baldacci & Philippe Bergault & Dylan Possamai, 2022. "A mean-field game of market-making against strategic traders," Papers 2203.13053, arXiv.org.
    4. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant & Julien Guilbert, 2024. "Automated Market Making: the case of Pegged Assets," Papers 2411.08145, arXiv.org.
    5. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant, 2022. "Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions," Papers 2212.00336, arXiv.org, revised Nov 2023.
    6. Robert Boyce & Martin Herdegen & Leandro S'anchez-Betancourt, 2024. "Market Making with Exogenous Competition," Papers 2407.17393, arXiv.org.
    7. Philippe Bergault & Olivier Gu'eant, 2023. "Liquidity Dynamics in RFQ Markets and Impact on Pricing," Papers 2309.04216, arXiv.org, revised Jun 2024.
    8. Marcello Monga, 2024. "Automated Market Making and Decentralized Finance," Papers 2407.16885, arXiv.org.
    9. Mathieu Rosenbaum & Jianfei Zhang, 2022. "Multi-asset market making under the quadratic rough Heston," Papers 2212.10164, arXiv.org.
    10. Alexander Barzykin & Philippe Bergault & Olivier Gu'eant, 2022. "Dealing with multi-currency inventory risk in FX cash markets," Papers 2207.04100, arXiv.org, revised Oct 2023.
    11. Zhou Fang & Haiqing Xu, 2023. "Market Making of Options via Reinforcement Learning," Papers 2307.01814, arXiv.org.
    12. Zhou Fang & Haiqing Xu, 2023. "Over-the-Counter Market Making via Reinforcement Learning," Papers 2307.01816, arXiv.org.

    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:taf:apmtfi:v:28:y:2021:i:2:p:101-142. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAMF20 .

    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.