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Optimal Fees for Liquidity Provision in Automated Market Makers

Author

Listed:
  • Steven Campbell
  • Philippe Bergault
  • Jason Milionis
  • Marcel Nutz

Abstract

Passive liquidity providers (LPs) in automated market makers (AMMs) face losses due to adverse selection (LVR), which static trading fees often fail to offset in practice. We study the key determinants of LP profitability in a dynamic reduced-form model where an AMM operates in parallel with a centralized exchange (CEX), traders route their orders optimally to the venue offering the better price, and arbitrageurs exploit price discrepancies. Using large-scale simulations and real market data, we analyze how LP profits vary with market conditions such as volatility and trading volume, and characterize the optimal AMM fee as a function of these conditions. We highlight the mechanisms driving these relationships through extensive comparative statics, and confirm the model's relevance through market data calibration. A key trade-off emerges: fees must be low enough to attract volume, yet high enough to earn sufficient revenues and mitigate arbitrage losses. We find that under normal market conditions, the optimal AMM fee is competitive with the trading cost on the CEX and remarkably stable, whereas in periods of very high volatility, a high fee protects passive LPs from severe losses. These findings suggest that a threshold-type dynamic fee schedule is both robust enough to market conditions and improves LP outcomes.

Suggested Citation

  • Steven Campbell & Philippe Bergault & Jason Milionis & Marcel Nutz, 2025. "Optimal Fees for Liquidity Provision in Automated Market Makers," Papers 2508.08152, arXiv.org.
    • Handle: RePEc:arx:papers:2508.08152
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    File URL: https://arxiv.org/pdf/2508.08152
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    References listed on IDEAS

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    1. 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.
    2. Leonardo Baggiani & Martin Herdegen & Leandro S'anchez-Betancourt, 2025. "Optimal Dynamic Fees in Automated Market Makers," Papers 2506.02869, arXiv.org, revised Jul 2026.
    3. 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.
    4. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Guéant & Julien Guilbert, 2024. "Price-Aware Automated Market Makers: Models Beyond Brownian Prices and Static Liquidity," Working Papers hal-04577060, HAL.
    5. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Guéant, 2024. "Automated market makers: mean-variance analysis of LPs payoffs and design of pricing functions," Digital Finance, Springer, vol. 6(2), pages 225-247, June.
    6. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant & Julien Guilbert, 2024. "Automated Market Making: the case of Pegged Assets," Papers 2411.08145, arXiv.org.
    7. Alif Aqsha & Philippe Bergault & Leandro S'anchez-Betancourt, 2025. "Equilibrium Reward for Liquidity Providers in Automated Market Makers," Papers 2503.22502, arXiv.org.
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    Citations

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    Cited by:

    1. Farbod Ghasemlu, 2026. "Optimal Dynamic Fees for Automated Market Makers: A Stochastic Control Approach to Loss-Versus-Rebalancing," Papers 2606.21769, arXiv.org.
    2. Leonardo Baggiani & Martin Herdegen & Leandro Sanchez-Betancourt, 2026. "Competition between DEXs through Dynamic Fees," Papers 2603.09669, arXiv.org.
    3. Philippe Bergault & S'ebastien Bieber & Leandro S'anchez-Betancourt, 2025. "Optimal Exit Time for Liquidity Providers in Automated Market Makers," Papers 2509.06510, arXiv.org, revised Oct 2025.
    4. Sunghun Ko, 2026. "Partially Active Automated Market Makers," Papers 2602.09887, arXiv.org.
    5. Wen-Ting Wang, 2026. "Reinforcement Learning for Execution under Dynamic Fees in a Closed-Loop DEX Simulator," Papers 2607.10960, arXiv.org.
    6. Philippe Bergault & Yadh Hafsi & Leandro S'anchez-Betancourt, 2026. "Trading in CEXs and DEXs with Priority Fees and Stochastic Delays," Papers 2602.10798, arXiv.org, revised Feb 2026.

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