Differential Liquidity Provision in Uniswap v3 and Implications for Contract Design

TL;DR

This paper analyzes how Uniswap v3's differential liquidity provision affects profit, trade execution, and contract design, showing that diverse price partitions benefit both providers and traders.

Contribution

It formalizes liquidity provider profits in Uniswap v3 and explores optimal price partitioning for contract design to enhance market efficiency.

Findings

Diverse price partitions improve liquidity and trading outcomes.

Optimal liquidity allocation depends on price evolution beliefs.

Flexible contract design benefits both providers and traders.

Abstract

Decentralized exchanges (DEXs) provide a means for users to trade pairs of assets on-chain without the need for a trusted third party to effectuate a trade. Amongst these, constant function market maker DEXs such as Uniswap handle the most volume of trades between ERC-20 tokens. With the introduction of Uniswap v3, liquidity providers can differentially allocate liquidity to trades that occur within specific price intervals. In this paper, we formalize the profit and loss that liquidity providers can earn when providing specific liquidity allocations to a v3 contract. We give a convex stochastic optimization problem for computing optimal liquidity allocation for a liquidity provider who holds a belief on how prices will evolve over time and use this to study the design question regarding how v3 contracts should partition the price space for permissible liquidity allocations. Our results show that making a greater diversity of price-space partitions available to a contract designer can simultaneously benefit both liquidity providers and traders.