  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.
