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Optimal market making

Author

Listed:
  • Olivier Guéant

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique)

Abstract

Market makers provide liquidity to other market participants: they propose prices at which they stand ready to buy and sell a wide variety of assets. They face a complex optimization problem with static and dynamic components: they need indeed to propose bid and offer/ask prices in an optimal way for making money out of the difference between these two prices (their bid-ask spread), while mitigating the risk associated with price changes -- because they seldom buy and sell simultaneously, and therefore hold long or short inventories which expose them to market risk. In this paper, (i) we propose a general modeling framework which generalizes (and reconciles) the various modeling approaches proposed in the literature since the publication of the seminal paper ``High-frequency trading in a limit order book'' by Avellaneda and Stoikov, (ii) we prove new general results on the existence and the characterization of optimal market making strategies, (iii) we obtain new closed-form approximations for the optimal quotes, (iv) we extend the modeling framework to the case of multi-asset market making, and (v) we show how the model can be used in practice in the specific case of the corporate bond market and for two credit indices.

Suggested Citation

  • Olivier Guéant, 2017. "Optimal market making," Post-Print hal-02862554, HAL.
    • Handle: RePEc:hal:journl:hal-02862554
    DOI: 10.1080/1350486X.2017.1342552
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    Citations

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    Cited by:

    1. Nicolas Baradel & Bruno Bouchard & David Evangelista & Othmane Mounjid, 2019. "Optimal inventory management and order book modeling," Post-Print hal-01710301, HAL.
    2. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2020. "How to build a cross-impact model from first principles: Theoretical requirements and empirical results," Working Papers hal-02567489, HAL.
    3. Philippe Bergault & Olivier Gu'eant, 2019. "Size matters for OTC market makers: general results and dimensionality reduction techniques," Papers 1907.01225, arXiv.org, revised Sep 2022.
    4. Lester Ingber, 2020. "Developing Bid-Ask Probabilities for High-Frequency Trading," Virtual Economics, The London Academy of Science and Business, vol. 3(2), pages 7-24, April.
    5. Mehdi Tomas & Iacopo Mastromatteo & Michael Benzaquen, 2020. "How to build a cross-impact model from first principles: Theoretical requirements and empirical results," Papers 2004.01624, arXiv.org, revised Mar 2022.
    6. Nicolas Baradel & Bruno Bouchard & David Evangelista & Othmane Mounjid, 2018. "Optimal inventory management and order book modeling," Working Papers hal-01710301, HAL.
    7. Bastien Baldacci & Philippe Bergault & Olivier Gu'eant, 2019. "Algorithmic market making for options," Papers 1907.12433, arXiv.org, revised Jul 2020.
    8. Nicolas Baradel & Bruno Bouchard & David Evangelista & Othmane Mounjid, 2018. "Optimal inventory management and order book modeling," Papers 1802.08135, arXiv.org, revised Nov 2018.
    9. Yagna Patel, 2018. "Optimizing Market Making using Multi-Agent Reinforcement Learning," Papers 1812.10252, arXiv.org.
    10. L. Ingber, 2020. "Forecasting with importance-sampling and path-integrals: Applications to COVID-19," Lester Ingber Papers 20fi, Lester Ingber.

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