Optimal Fees for Liquidity Provision in Automated Market Makers

2025-08-11

AI Summary

Passive liquidity providers (LPs) in automated market makers (AMMs) suffer persistent losses from adverse selection—specifically, loss-versus-rebalancing (LVR)—which static fee structures fail to offset adequately. Method: We develop a dynamic equilibrium model that quantifies how volatility and trading volume jointly affect LP profitability. We propose a threshold-based dynamic fee mechanism: low baseline fees under normal conditions to incentivize trading activity, with automatic fee increases during high-volatility regimes to curb arbitrage-driven losses. Our approach integrates real-market data calibration, parallel trading modeling across centralized exchanges (CEXs), optimal order routing, and realistic arbitrage behavior simulation, followed by comparative static analysis. Results: The mechanism significantly improves LP returns; fee adjustments exhibit robust, state-contingent patterns; and its cost efficiency matches—or even surpasses—that of CEXs. This work provides an interpretable, deployable theoretical foundation and practical framework for incentive-aligned liquidity provision in AMMs.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Cryptocurrency and smart contracts

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.

Problem

• Determining optimal fees for liquidity providers in AMMs
• Analyzing LP profitability under varying market conditions
• Balancing fee levels to attract volume and mitigate losses

Innovation

• Dynamic fee schedule optimizes LP profitability
• Threshold-type fees adapt to market volatility
• Calibration with real data ensures model relevance