Unified Approach for Hedging Impermanent Loss of Liquidity Provision

Alexander Lipton, Vladimir Lucic and Artur Sepp

Papers from arXiv.org

Abstract: We develop static model-independent and dynamic model-dependent 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 the different definitions occurring in the existing literature. We show that the IL can be seen as a contingent claim with a non-linear pay-off for a fixed maturity date. Thus, we introduce the contingent claim termed the IL protection claim which delivers the negative of IL pay-off at the maturity date. We apply arbitrage-based methods for the 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 generalise 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 the IL protection claim under the Black-Scholes-Merton model and the log-normal stochastic volatility model. We finally discuss the estimation of the risk-reward of LP staking using our results.

Date: 2024-07, Revised 2026-10
New Economics Papers: this item is included in nep-mac and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://arxiv.org/pdf/2407.05146 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2407.05146

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().