An Economic Model of a Decentralized Exchange with Concentrated Liquidity

Abstract

We develop an economic model of a decentralized exchange with concentrated liquidity (i.e., Uniswap V3) with a particular focus on the economics of liquidity provision. We demonstrate that providing liquidity for a risky/risk-free asset pool is comparable to investing in a covered call except that the call option therein is sold at intrinsic rather than market value. Hence, when providing liquidity, liquidity providers forgo the time premium of the call option in exchange for fees and thus equilibrium liquidity provision decreases in the time premium. Finally, we provide an expression for equilibrium liquidity provision which is useful for empirical work.

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

JEL Classification: G10, G12