Optimal Fees for Liquidity Provision in Automated Market Makers

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.