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Chasing price drains liquidity

Author

Listed:
  • Yizhou Cao

    (Derivation Technology Ltd.)

  • Yepeng Ding

    (Hiroshima University)

  • Ruichao Jiang

    (Derivation Technology Ltd.)

  • Long Wen

    (POLYU - The Hong Kong Polytechnic University [Hong Kong])

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.

Suggested Citation

  • Yizhou Cao & Yepeng Ding & Ruichao Jiang & Long Wen, 2025. "Chasing price drains liquidity," Working Papers hal-04872864, HAL.
    • Handle: RePEc:hal:wpaper:hal-04872864
    Note: View the original document on HAL open archive server: https://hal.science/hal-04872864v1
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