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Closed-form Approximations in Multi-asset Market Making

Author

Listed:
  • Philippe Bergault

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Olivier Guéant

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • David Evangelista

    (FGV/EMAp - Fundação Getulio Vargas - Escola de Matemática Aplicada [Rio de Janeiro])

  • Douglas Vieira

    (Imperial College London)

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 & Olivier Guéant & David Evangelista & Douglas Vieira, 2021. "Closed-form Approximations in Multi-asset Market Making," Post-Print hal-03680074, HAL.
    • Handle: RePEc:hal:journl:hal-03680074
    DOI: 10.1080/1350486X.2021.1949359
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    Cited by:

    1. 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.
    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, 2022. "Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions," Papers 2212.00336, arXiv.org, revised Nov 2023.
    5. Robert Boyce & Martin Herdegen & Leandro S'anchez-Betancourt, 2024. "Market Making with Exogenous Competition," Papers 2407.17393, arXiv.org.
    6. Philippe Bergault & Olivier Gu'eant, 2023. "Liquidity Dynamics in RFQ Markets and Impact on Pricing," Papers 2309.04216, arXiv.org, revised Jun 2024.
    7. Marcello Monga, 2024. "Automated Market Making and Decentralized Finance," Papers 2407.16885, arXiv.org.
    8. Mathieu Rosenbaum & Jianfei Zhang, 2022. "Multi-asset market making under the quadratic rough Heston," Papers 2212.10164, arXiv.org.
    9. 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.
    10. Zhou Fang & Haiqing Xu, 2023. "Market Making of Options via Reinforcement Learning," Papers 2307.01814, arXiv.org.
    11. Zhou Fang & Haiqing Xu, 2023. "Over-the-Counter Market Making via Reinforcement Learning," Papers 2307.01816, arXiv.org.

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