The Term Structure of Implied Fee Rates in Liquidity Pools

Paper: arXiv 2610.36392

Authors: Diogo Duarte, Lucas X. Ferreira, Emmanuel Gobet, Yuri F. Saporito

Abstract

We develop a no-arbitrage framework to recover implied fee rates from option-implied information and quantify fee compensation for liquidity providers in automated market maker (AMM) pools. Expected accumulated fees equal the current pool value minus the risk-neutral value of its terminal payoff, reducing forward-looking LP compensation to pricing the LP payoff. We apply the framework to Uniswap v2 and Uniswap v3 ETH–USDC pools using a stochastic-volatility jump-diffusion model calibrated to Deribit options. Implied fee rates are positive, time varying, downward sloping in maturity, and highly sensitive to range design, with tighter near-the-money ranges earning larger implied returns.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a sophisticated no-arbitrage framework using stochastic-volatility jump-diffusion models, demonstrating high mathematical complexity. It applies this framework to real-world Uniswap data and Deribit options, showing strong empirical rigor. The novel approach of recovering implied fee rates from option-implied information is a significant contribution to DeFi research.

Research Flowchart

  flowchart TD
    A[Research Goal: Quantify LP Compensation & Implied Fee Rates] --> B{Methodology: No-Arbitrage Framework};
    B --> C[Data/Inputs: Uniswap v2/v3 ETH-USDC Pools, Deribit Options];
    C --> D{Computational Process: Calibrate Stochastic Volatility Jump-Diffusion Model};
    D --> E[Outcome 1: Implied Fee Rates are Positive, Time Varying, Downward Sloping];
    D --> F[Outcome 2: Fee Rates Highly Sensitive to Range Design (tighter ranges = larger returns)];
    E & F --> G[Conclusion: Developed framework for pricing LP payoff & assessing compensation];