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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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    Citations

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    Cited by:

    1. 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.
    2. Philippe Bergault & Olivier Gu'eant, 2023. "Modeling liquidity in corporate bond markets: applications to price adjustments," Papers 2309.04216, arXiv.org, revised Oct 2023.
    3. Mathieu Rosenbaum & Jianfei Zhang, 2022. "Multi-asset market making under the quadratic rough Heston," Papers 2212.10164, arXiv.org.
    4. 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.
    5. Zhou Fang & Haiqing Xu, 2023. "Market Making of Options via Reinforcement Learning," Papers 2307.01814, arXiv.org.
    6. Zhou Fang & Haiqing Xu, 2023. "Over-the-Counter Market Making via Reinforcement Learning," Papers 2307.01816, arXiv.org.

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