Implied Impermanent Loss: A Cross-Sectional Analysis of Decentralized Liquidity Pools

Abstract

We derive an option-implied valuation of impermanent loss for liquidity providers on decentralized exchanges and quantify it based on traded option prices. We propose a model that values impermanent loss through the variance of the tokens' relative price. Since the relative price is not the price of a traded asset, we introduce a model for the distribution of the former and a valuation formula induced by a change of numéraire. We show that impermanent loss arises from the tokens' individual risks and their correlation risk. These risks negatively impact pool sizes and explain the cross-sectional returns of liquidity pools. 

Keywords: Decentralized Exchanges, Decentralized Finance, Impermanent Loss, Derivatives, Risk-Neutral Pricing, Staking

JEL Classification: G10, G11, G13, G20