An Economic Model of a Decentralized Exchange with Concentrated Liquidity

Abstract

We provide an economic model of a decentralized exchange (DEX) that allows investors to concentrate liquidity within exogenously specified price intervals (e.g., Uniswap V3). We demonstrate that providing liquidity for a risky vs. risk-free asset pair within any price interval is analogous to investing in a portfolio composed of the risky asset and the risk-free asset subject to a further cost due to arbitrage trading against the DEX. The associated portfolio weights evolve dynamically such that the risky asset portfolio weight declines from unity to zero as the risky asset price increases. Moreover, DEX liquidity provision is always a sub-optimal investment in the absence of trading fees. In turn, we show that any level of positive trading fees supports a unique level of equilibrium liquidity provision for each DEX price interval. We provide a simple approximation of the equilibrium liquidity provision for each interval which can be useful for empirical work. We also demonstrate that liquidity provision to an interval provides a return approximately equivalent to a covered call trading strategy.

Keywords: Decentralized Exchange, DEX, Automated Market Makers, AMM, Concentrated Liquidity, Uniswap V3

JEL Classification: G10, G12