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Optimal Fees for Liquidity Provision in Automated Market Makers

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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: http://arxiv.org/pdf/2508.08152
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    References listed on IDEAS

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    1. Leonardo Baggiani & Martin Herdegen & Leandro S'anchez-Betancourt, 2025. "Optimal Dynamic Fees in Automated Market Makers," Papers 2506.02869, arXiv.org, revised Jun 2025.
    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. 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.
    4. Alif Aqsha & Philippe Bergault & Leandro S'anchez-Betancourt, 2025. "Equilibrium Reward for Liquidity Providers in Automated Market Makers," Papers 2503.22502, arXiv.org.
    5. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Guéant & Julien Guilbert, 2024. "Price-Aware Automated Market Makers: Models Beyond Brownian Prices and Static Liquidity," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-04577060, HAL.
    6. 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.
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    Cited by:

    1. 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.

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