Static Replication of Impermanent Loss for Concentrated Liquidity Provision in Decentralised Markets

Abstract

This article analytically characterizes the impermanent loss of concentrated liquidity provision for automatic market makers in decentralised markets such as Uniswap. We propose two static replication formulas for the impermanent loss by a combination of European calls or puts with strike prices supported on the liquidity provision price interval. It facilitates liquidity providers to hedge permanent loss by trading crypto options in more liquid centralised exchanges such as Deribit. Numerical examples illustrate the astonishing accuracy of the static replication.