The Implied Impermanent Loss in Decentralized Liquidity Provision

We derive an option-implied valuation of impermanent loss, quantifying the risk to liquidity providers on decentralized exchanges. Our valuation is 1/8 times the variance-swap rate of the tokens' relative price. Options on relative price do not trade, but we impose a distribution for it, subject to constraints from options on the individual tokens. We document an impermanent loss premium—the difference between implied and realized impermanent loss—that compensates liquidity providers for exposure to impermanent loss, captures the variance and correlation premia of the underlying tokens, and is strongly correlated with pool returns and size.