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Dynamics of Liquidity Surfaces in Uniswap v3

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  • Jimmy Risk
  • Shen-Ning Tung
  • Tai-Ho Wang

Abstract

This paper presents a comprehensive study on the empirical dynamics of Uniswap v3 liquidity, which we model as a time-tick surface, $L_t(x)$. Using a combination of functional principal component analysis (FPCA) and dynamic factor methods, we analyze three distinct pools over multiple sample periods. Our findings offer three main contributions: a statistical characterization of automated market maker liquidity, an interpretable and portable basis for dimension reduction, and a robust analysis of liquidity dynamics using rolling window metrics. For the 5 bps pools, the leading empirical eigenfunctions explain the majority of cross-tick variation and remain stable, aligning closely with a low-order Legendre polynomial basis. This alignment provides a parsimonious and interpretable structure, similar to the dynamic Nelson-Siegel method for yield curves. The factor coefficients exhibit a time series structure well-captured by AR(1) models with clear GARCH-type heteroskedasticity and heavy-tailed innovations.

Suggested Citation

  • Jimmy Risk & Shen-Ning Tung & Tai-Ho Wang, 2025. "Dynamics of Liquidity Surfaces in Uniswap v3," Papers 2509.05013, arXiv.org.
    • Handle: RePEc:arx:papers:2509.05013
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    1. Daniele Maria Di Nosse & Federico Gatta & Fabrizio Lillo & Sebastian Jaimungal, 2025. "Deviations from Tradition: Stylized Facts in the Era of DeFi," Papers 2510.22834, arXiv.org.

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