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

2025-09-27

AI Summary

Quantifying liquidity provider (LP) risk in automated market makers (AMMs) remains challenging, particularly due to the path-dependent nature of impermanent loss (IL). Method: This paper reinterprets IL as an implicit fee stream under risk-neutral valuation, rendering LPs indifferent between providing liquidity and holding assets. Building on this, we design a novel fixed-for-floating swap contract—priced using actual AMM fee revenues—to quote implied volatility and implied correlation of digital assets. Our approach integrates IL theory, risk-neutral pricing, and derivative design, and is empirically validated using on-chain fee data. Contribution/Results: We derive a fee-implied volatility metric that exhibits strong predictive power and economic interpretability. To our knowledge, this constitutes the first tradable, hedgeable implied volatility benchmark for decentralized finance (DeFi), accompanied by a native risk management framework. The methodology enables systematic volatility exposure and correlation trading in AMM-based markets.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Reinterpreting loss-versus-rebalancing as implied AMM fee stream
• Proposing a swap to quote implied volatilities of digital assets
• Empirically validating fee-based volatility relevance across markets

Innovation

• Reinterprets loss-versus-rebalancing as implied fee stream
• Proposes fixed-for-floating swap on AMM fees
• Quotes implied volatilities and correlations of assets