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Closed-form Approximations in Multi-asset Market Making

Author

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  • 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
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    Cited by:

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

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