Chasing price drains liquidity
Computational Engineering, Finance, and Science
2025-01-23 v1
Abstract
Assuming that the price in a Uniswap v3 style Automated Market Maker (AMM) follows a Geometric Brownian Motion (GBM), we prove that the strategy that adjusts the position of liquidity to track the current price leads to a deterministic and exponentially fast decay of liquidity. Next, assuming that there is a Centralized Exchange (CEX), in which the price follows a GBM and the AMM price mean reverts to the CEX price, we show numerically that the same strategy still leads to decay. Last, we propose a strategy that increases the liquidity even without compounding fees earned through liquidity provision.
Cite
@article{arxiv.2501.12583,
title = {Chasing price drains liquidity},
author = {Yizhou Cao and Yepeng Ding and Ruichao Jiang and Long Wen},
journal= {arXiv preprint arXiv:2501.12583},
year = {2025}
}