Unified Approach for Hedging Impermanent Loss of Liquidity Provision

TL;DR

This paper introduces a unified framework for hedging impermanent loss in liquidity provision on DEXes, using static and dynamic models, and provides explicit valuation formulas under various market assumptions.

Contribution

It develops a comprehensive approach to quantify and hedge impermanent loss, unifying different definitions and applying arbitrage-based methods with explicit formulas.

Findings

IL can be modeled as a contingent claim with a non-linear payoff.

Perfect hedging of IL is possible with options in liquid markets.

Analytic valuation formulas are derived under Black-Scholes-Merton and stochastic volatility models.

Abstract

We develop static and dynamic approaches for hedging of the impermanent loss (IL) of liquidity provision (LP) staked at Decentralised Exchanges (DEXes) which employ Uniswap V2 and V3 protocols. We provide detailed definitions and formulas for computing the IL to unify different definitions occurring in the existing literature. We show that the IL can be seen a contingent claim with a non-linear payoff for a fixed maturity date. Thus, we introduce the contingent claim termed as IL protection claim which delivers the negative of IL payoff at the maturity date. We apply arbitrage-based methods for valuation and risk management of this claim. First, we develop the static model-independent replication method for the valuation of IL protection claim using traded European vanilla call and put options. We extend and generalize an existing method to show that the IL protection claim can be hedged perfectly with options if there is a liquid options market. Second, we develop the dynamic model-based approach for the valuation and hedging of IL protection claims under a risk-neutral measure. We derive analytic valuation formulas using a wide class of price dynamics for which the characteristic function is available under the risk-neutral measure. As base cases, we derive analytic valuation formulas for IL protection claim under the Black-Scholes-Merton model and the log-normal stochastic volatility model. We finally discuss estimation of risk-reward of LP staking using our results.