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Optimal market making

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  • Olivier Guéant

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 both 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). Since they seldom buy and sell simultaneously, and therefore hold long and/or short inventories, they also need to mitigate the risk associated with price changes and subsequently skew their quotes dynamically. In this paper, (i) we propose a general modelling framework which generalizes (and reconciles) the various modelling 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 modelling framework to the case of multi-asset market making and we obtain general closed-form approximations for the optimal quotes of a multi-asset market maker, and (v) we show how the model can be used in practice in the specific (and original) case of two credit indices.

Suggested Citation

  • Olivier Guéant, 2017. "Optimal market making," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(2), pages 112-154, March.
    • Handle: RePEc:taf:apmtfi:v:24:y:2017:i:2:p:112-154
    DOI: 10.1080/1350486X.2017.1342552
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    Cited by:

    1. 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.
    2. Bastien Baldacci & Philippe Bergault & Olivier Gu'eant, 2019. "Algorithmic market making for options," Papers 1907.12433, arXiv.org, revised Jul 2020.
    3. Fr'ed'eric Abergel & C^ome Hur'e & Huy^en Pham, 2017. "Algorithmic trading in a microstructural limit order book model," Papers 1705.01446, arXiv.org, revised Feb 2020.
    4. Nicolas Baradel & Bruno Bouchard & David Evangelista & Othmane Mounjid, 2018. "Optimal inventory management and order book modeling," Working Papers hal-01710301, HAL.
    5. Yagna Patel, 2018. "Optimizing Market Making using Multi-Agent Reinforcement Learning," Papers 1812.10252, arXiv.org.
    6. Nicolas Baradel & Bruno Bouchard & David Evangelista & Othmane Mounjid, 2019. "Optimal inventory management and order book modeling," Post-Print hal-01710301, HAL.
    7. 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.
    8. L. Ingber, 2020. "Forecasting with importance-sampling and path-integrals: Applications to COVID-19," Lester Ingber Papers 20fi, Lester Ingber.
    9. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    10. 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.
    11. Vincent Ragel & Damien Challet, 2024. "Data time travel and consistent market making: taming reinforcement learning in multi-agent systems with anonymous data," Papers 2408.02322, arXiv.org.
    12. 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.
    13. Frédéric Abergel & Côme Huré & Huyên Pham, 2019. "Algorithmic trading in a microstructural limit order book model," Working Papers hal-01514987, HAL.
    14. Nicolas Baradel & Bruno Bouchard & David Evangelista & Othmane Mounjid, 2018. "Optimal inventory management and order book modeling," Papers 1802.08135, arXiv.org, revised Nov 2018.
    15. Joseph Jerome & Leandro Sanchez-Betancourt & Rahul Savani & Martin Herdegen, 2022. "Model-based gym environments for limit order book trading," Papers 2209.07823, arXiv.org.

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