The Price of Liquidity: Implied Volatility of Automated Market Maker Fees

Paper: arXiv 2509.23222

Authors: Maxim Bichuch, Zachary Feinstein

Abstract

An automated market maker (AMM) provides a method for creating a decentralized exchange on the blockchain. For this purpose, individual investors lend liquidity to the AMM pool in exchange for a stream of fees earned from its operations as a market maker. Within this work, we reinterpret the loss-versus-rebalancing as the implied fee stream generated by an AMM so that a risk-neutral investor is indifferent in the decision of providing liquidity. With this implied fee structure, we propose a novel fixed-for-floating swap on the fees generated by an AMM in order to quote the implied volatilities and implied correlations of digital assets. We apply this theory to realized fees in different markets to empirically validate the relevance of the deduced fee-based volatility.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical framework reinterpreting Loss-Versus-Rebalancing (LVR) into an implied fee stream for AMMs to price novel fixed-for-floating swaps. It supports this strong theoretical contribution with initial empirical validation on Uniswap v3 and high-frequency SPY simulation data.

Research Flowchart

  flowchart TD
    A[Research Goal: Quote Implied Volatility & Correlation via AMM Fees] --> B[Reinterpret Loss-Versus-Rebalancing LVR as Implied Fee Stream]
    B --> C[Design Fixed-for-Floating Swap on AMM Generated Fees]
    D[Input: Realized AMM Fees & Digital Asset Market Data] --> E[Apply Swap Theory to Calculate Implied Volatility & Correlation]
    C --> E
    E --> F[Empirical Validation Across Different Crypto Markets]
    F --> G[Outcome: Validated Fee-Based Volatility Framework for Digital Assets]