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Optimal Dynamic Fees in Automated Market Makers

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  • Leonardo Baggiani
  • Martin Herdegen
  • Leandro S'anchez-Betancourt

Abstract

Automated Market Makers (AMMs) are emerging as a popular decentralised trading platform. In this work, we determine the optimal dynamic fees in a constant function market maker. We find approximate closed-form solutions to the control problem and study the optimal fee structure. We find that there are two distinct fee regimes: one in which the AMM imposes higher fees to deter arbitrageurs, and another where fees are lowered to increase volatility and attract noise traders. Our results also show that dynamic fees that are linear in inventory and are sensitive to changes in the external price are a good approximation of the optimal fee structure and thus constitute suitable candidates when designing fees for AMMs.

Suggested Citation

  • Leonardo Baggiani & Martin Herdegen & Leandro S'anchez-Betancourt, 2025. "Optimal Dynamic Fees in Automated Market Makers," Papers 2506.02869, arXiv.org.
    • Handle: RePEc:arx:papers:2506.02869
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    References listed on IDEAS

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    1. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    2. Álvaro Cartea & Fayçal Drissi & Marcello Monga, 2023. "Predictable Losses of Liquidity Provision in Constant Function Markets and Concentrated Liquidity Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(2), pages 69-93, March.
    3. Emilio Barucci & Adrien Mathieu & Leandro S'anchez-Betancourt, 2025. "Market Making with Fads, Informed, and Uninformed Traders," Papers 2501.03658, arXiv.org, revised Feb 2025.
    4. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
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