Chasing price drains liquidity

Yizhou Cao, Yepeng Ding (), Ruichao Jiang and Long Wen ()
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Yizhou Cao: Derivation Technology Ltd.
Yepeng Ding: Hiroshima University
Ruichao Jiang: Derivation Technology Ltd.
Long Wen: POLYU - The Hong Kong Polytechnic University [Hong Kong]

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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.

Date: 2025-01-08
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