Optimal Fees for Liquidity Provision in Automated Market Makers

Paper: arXiv 2508.08152

Authors: 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.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs a sophisticated dynamic reduced-form model with geometric Brownian motion and comparative statics, while also using large-scale simulations calibrated with real market data and providing open-source code for reproducibility.

Research Flowchart

  flowchart TD
  A["Research Goal:<br/>Determine Optimal AMM Fee<br/>to Maximize LP Profit"] --> B["Methodology: Dynamic Reduced-Form Model<br/>+ Large-Simulations & Real Data"]
  B --> C["Key Inputs:<br/>Volatility, Trading Volume<br/>CEX Costs, Price Drift"]
  C --> D["Computational Process:<br/>Optimal Fee Search<br/>over Trading & Arbitrage Constraints"]
  D --> E["Key Outcome 1:<br/>Optimal Fee ≈ CEX Cost<br/>in Normal Markets"]
  D --> F["Key Outcome 2:<br/>Optimal Fee ↑ sharply<br/>in High Volatility"]
  E --> G["Recommendation:<br/>Adopt Dynamic Fee Schedule<br/>(Low in calm, High in volatile periods)"]

Cited References (142)

1. Learning from DeFi : Would Automated Market Makers Improve Equity Trading? (2026) — link
2. The viability of blockchain markets under discrete clearing and paid priority (2026) — link
3. Optimal Dynamic Fees in Automated Market Makers (2025) — link
4. Liquidity provision and its information content in decentralized markets (2026) — link
5. The Impact of Market Conditions and Fee Algorithms on the Design of a Competitive AMM (2024) — link
6. Decentralized Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision (2024)
7. Coexisting Exchange Platforms: Limit Order Books and Automated Market Makers (2025) — link
8. Optimal Design of Automated Market Makers on Decentralized Exchanges (2024) — link

6 of 142 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.