Unified Approach for Hedging Impermanent Loss of Liquidity Provision

ArXiv ID: 2407.05146 “View on arXiv”

Authors: Unknown

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.

Keywords: impermanent loss (IL), liquidity provision, contingent claims, option hedging, Uniswap, Cryptocurrency / DeFi

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper relies heavily on advanced stochastic calculus, analytic solution derivations under specific models (BSM, Heston, log-normal SV), and arbitrage-based replication theory, indicating high mathematical density. However, it lacks empirical validation such as backtests, statistical metrics, or data-driven implementation examples, focusing instead on theoretical valuation and hedging frameworks.

  flowchart TD
    A["Research Goal<br>Quantify & Hedge Impermanent Loss in DeFi LPs"] --> B["Define IL as Contingent Claim"]
    B --> C["Methodology 1: Static Model-Independent<br>Replication via Options"]
    B --> D["Methodology 2: Dynamic Model-Based<br>Valuation under Risk-Neutral Measure"]
    C --> E["Outcomes: Perfect Hedge with Liquid Options<br>Extension of Existing Methods"]
    D --> F["Outcomes: Analytic Valuation Formulas<br>e.g., Black-Scholes & Stochastic Volatility"]
    E --> G["Unified Framework & Risk-Reward Estimation"]
    F --> G