IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2509.05013.html
   My bibliography  Save this paper

Dynamics of Liquidity Surfaces in Uniswap v3

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2509.05013
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Christensen, Jens H.E. & Diebold, Francis X. & Rudebusch, Glenn D., 2011. "The affine arbitrage-free class of Nelson-Siegel term structure models," Journal of Econometrics, Elsevier, vol. 164(1), pages 4-20, September.
    2. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    3. Weibing Huang & Charles-Albert Lehalle & Mathieu Rosenbaum, 2015. "Simulating and Analyzing Order Book Data: The Queue-Reactive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 107-122, March.
    4. Carol Alexander & Xi Chen & Jun Deng & Qi Fu, 2025. "Price Discovery and Efficiency in Uniswap Liquidity Pools," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 45(8), pages 1023-1048, August.
    5. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
    6. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    7. Andreea Oprea, 2022. "The Use of Principal Component Analysis (PCA) in Building Yield Curve Scenarios and Identifying Relative-Value Trading Opportunities on the Romanian Government Bond Market," JRFM, MDPI, vol. 15(6), pages 1-37, May.
    8. Hugo Hissinaga & Márcio Laurini, 2024. "Interest Rate Forecasting with Principal Component Analysis Based on Long-Run Covariance Matrix," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-50, June.
    9. 'Alvaro Cartea & Fayc{c}al Drissi & Marcello Monga, 2023. "Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision," Papers 2309.08431, arXiv.org, revised Jun 2024.
    10. Siegfried Hörmann & Łukasz Kidziński & Marc Hallin, 2015. "Dynamic functional principal components," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 319-348, March.
    11. Elie Kapengut & Bruce Mizrach, 2023. "An Event Study of the Ethereum Transition to Proof-of-Stake," Commodities, MDPI, vol. 2(2), pages 1-15, March.
    12. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    13. Deborah Miori & Mihai Cucuringu, 2024. "Clustering Uniswap v3 traders from their activity on multiple liquidity pools, via novel graph embeddings," Digital Finance, Springer, vol. 6(1), pages 113-143, March.
    14. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    15. Rama Cont & Marvin S. Mueller, 2019. "A stochastic partial differential equation model for limit order book dynamics," Papers 1904.03058, arXiv.org, revised May 2021.
    16. Stock, James H. & Watson, Mark, 2011. "Dynamic Factor Models," Scholarly Articles 28469541, Harvard University Department of Economics.
    17. Marco Avellaneda & Brian Healy & Andrew Papanicolaou & George Papanicolaou, 2020. "PCA for Implied Volatility Surfaces," Papers 2002.00085, arXiv.org.
    18. Agostino Capponi & Ruizhe Jia, 2021. "The Adoption of Blockchain-based Decentralized Exchanges," Papers 2103.08842, arXiv.org, revised Jul 2021.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Manfred Gilli & Enrico Schumann, 2012. "Heuristic optimisation in financial modelling," Annals of Operations Research, Springer, vol. 193(1), pages 129-158, March.
    2. Shi, Yukun & Stasinakis, Charalampos & Xu, Yaofei & Yan, Cheng, 2022. "Market co-movement between credit default swap curves and option volatility surfaces," International Review of Financial Analysis, Elsevier, vol. 82(C).
    3. Francesco Campigli & Gabriele Tedeschi & Maria Cristina Recchioni, 2021. "The talkative variables of the hybrid Heston model: Yields’ maturity and economic (in)stability," Working Papers 2021/03, Economics Department, Universitat Jaume I, Castellón (Spain).
    4. Kearney, Fearghal & Shang, Han Lin & Sheenan, Lisa, 2019. "Implied volatility surface predictability: The case of commodity markets," Journal of Banking & Finance, Elsevier, vol. 108(C).
    5. Detlefsen, Kai & Härdle, Wolfgang Karl, 2006. "Forecasting the term structure of variance swaps," SFB 649 Discussion Papers 2006-052, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Norman R. Swanson & Weiqi Xiong, 2018. "Big data analytics in economics: What have we learned so far, and where should we go from here?," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(3), pages 695-746, August.
    7. João Frois Caldeira & Rangan Gupta & Muhammad Tahir Suleman & Hudson S. Torrent, 2021. "Forecasting the Term Structure of Interest Rates of the BRICS: Evidence from a Nonparametric Functional Data Analysis," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 57(15), pages 4312-4329, December.
    8. Massimo Guidolin & Manuela Pedio, 2019. "Forecasting and Trading Monetary Policy Effects on the Riskless Yield Curve with Regime Switching Nelson†Siegel Models," Working Papers 639, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    9. Hong, Zhiwu & Niu, Linlin & Zhang, Chen, 2022. "Affine arbitrage-free yield net models with application to the euro debt crisis," Journal of Econometrics, Elsevier, vol. 230(1), pages 201-220.
    10. Ioannis A. Venetis & Avgoustinos Ladas, 2023. "Co-movement and global factors in sovereign bond yields," Bulletin of Applied Economics, Risk Market Journals, vol. 10(2), pages 17-45.
    11. P. Byrne, Joseph & Cao, Shuo & Korobilis, Dimitris, 2015. "Term Structure Dynamics, Macro-Finance Factors and Model Uncertainty," SIRE Discussion Papers 2015-71, Scottish Institute for Research in Economics (SIRE).
    12. repec:hum:wpaper:sfb649dp2007-023 is not listed on IDEAS
    13. Alexander Tsyplakov, 2011. "An introduction to state space modeling (in Russian)," Quantile, Quantile, issue 9, pages 1-24, July.
    14. Kaya, Huseyin, 2013. "Forecasting the yield curve and the role of macroeconomic information in Turkey," Economic Modelling, Elsevier, vol. 33(C), pages 1-7.
    15. Donati, Paola & Donati, Francesco, 2008. "Modelling and Forecasting the Yield Curve under Model uncertainty," Working Paper Series 917, European Central Bank.
    16. Gauthier, Geneviève & Simonato, Jean-Guy, 2012. "Linearized Nelson–Siegel and Svensson models for the estimation of spot interest rates," European Journal of Operational Research, Elsevier, vol. 219(2), pages 442-451.
    17. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2010. "Inflation Expectations and Risk Premiums in an Arbitrage‐Free Model of Nominal and Real Bond Yields," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(s1), pages 143-178, September.
    18. Laurini, Márcio P. & Caldeira, João F., 2016. "A macro-finance term structure model with multivariate stochastic volatility," International Review of Economics & Finance, Elsevier, vol. 44(C), pages 68-90.
    19. Philippe Bergault & Enzo Cogn'eville, 2024. "Simulating and analyzing a sparse order book: an application to intraday electricity markets," Papers 2410.06839, arXiv.org.
    20. Eo, Yunjong & Kang, Kyu Ho, 2020. "The effects of conventional and unconventional monetary policy on forecasting the yield curve," Journal of Economic Dynamics and Control, Elsevier, vol. 111(C).
    21. Hännikäinen, Jari, 2017. "When does the yield curve contain predictive power? Evidence from a data-rich environment," International Journal of Forecasting, Elsevier, vol. 33(4), pages 1044-1064.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2509.05013. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.