IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2409.11339.html
   My bibliography  Save this paper

DeFi Arbitrage in Hedged Liquidity Tokens

Author

Listed:
  • Maxim Bichuch
  • Zachary Feinstein

Abstract

Empirically, the prevailing market prices for liquidity tokens of the constant product market maker (CPMM) -- as offered in practice by companies such as Uniswap -- readily permit arbitrage opportunities by delta hedging the risk of the position. Herein, we investigate this arbitrage opportunity by treating the liquidity token as a derivative position in the prices of the underlying assets for the CPMM. In doing so, not dissimilar to the Black-Scholes result, we deduce risk-neutral pricing and hedging formulas for these liquidity tokens. Furthermore, with our novel pricing formula, we construct a method to calibrate a volatility to data which provides an updated (non-market) price which would not permit arbitrage if quoted by the CPMM. We conclude with a discussion of novel AMM designs which would bring the pricing of liquidity tokens into the modern financial era.

Suggested Citation

  • Maxim Bichuch & Zachary Feinstein, 2024. "DeFi Arbitrage in Hedged Liquidity Tokens," Papers 2409.11339, arXiv.org.
    • Handle: RePEc:arx:papers:2409.11339
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2409.11339
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wood, Robert A & McInish, Thomas H & Ord, J Keith, 1985. "An Investigation of Transactions Data for NYSE Stocks," Journal of Finance, American Finance Association, vol. 40(3), pages 723-739, July.
    2. Masaaki Fukasawa & Basile Maire & Marcus Wunsch, 2023. "Weighted variance swaps hedge against impermanent loss," Quantitative Finance, Taylor & Francis Journals, vol. 23(6), pages 901-911, June.
    3. Jin Hong Kuan, 2022. "Liquidity Provision Payoff on Automated Market Makers," Papers 2209.01653, arXiv.org.
    4. Álvaro Cartea & Fayçal Drissi & Marcello Monga, 2023. "Predictable Losses of Liquidity Provision in Constant Function Markets and Concentrated Liquidity Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 30(2), pages 69-93, March.
    5. Stefan Loesch & Nate Hindman & Mark B Richardson & Nicholas Welch, 2021. "Impermanent Loss in Uniswap v3," Papers 2111.09192, arXiv.org.
    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. Xilong Chen & Eric Ghysels, 2011. "News--Good or Bad--and Its Impact on Volatility Predictions over Multiple Horizons," The Review of Financial Studies, Society for Financial Studies, vol. 24(1), pages 46-81, October.
    2. Kari Harju & Syed Mujahid Hussain, 2011. "Intraday Seasonalities and Macroeconomic News Announcements," European Financial Management, European Financial Management Association, vol. 17(2), pages 367-390, March.
    3. Panayi, Efstathios & Peters, Gareth W. & Danielsson, Jon & Zigrand, Jean-Pierre, 2018. "Designating market maker behaviour in limit order book markets," Econometrics and Statistics, Elsevier, vol. 5(C), pages 20-44.
    4. Muchnik, Lev & Bunde, Armin & Havlin, Shlomo, 2009. "Long term memory in extreme returns of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4145-4150.
    5. Gerhard, Frank & Hess, Dieter & Pohlmeier, Winfried, 1998. "What a Difference a Day Makes: On the Common Market Microstructure of Trading Days," CoFE Discussion Papers 98/01, University of Konstanz, Center of Finance and Econometrics (CoFE).
    6. Denisa Banulescu-Radu & Christophe Hurlin & Bertrand Candelon & Sébastien Laurent, 2016. "Do We Need High Frequency Data to Forecast Variances?," Annals of Economics and Statistics, GENES, issue 123-124, pages 135-174.
    7. Bernhardt, Dan & Hughson, Eric, 2002. "Intraday trade in dealership markets," European Economic Review, Elsevier, vol. 46(9), pages 1697-1732, October.
    8. R. Baupain & A. Durre, 2007. "The interday and intraday patterns of the overnight market : evidence from an electronic platform," Post-Print hal-00300195, HAL.
    9. Ben Omrane, Walid & Hussain, Syed Mujahid, 2016. "Foreign news and the structure of co-movement in European equity markets: An intraday analysis," Research in International Business and Finance, Elsevier, vol. 37(C), pages 572-582.
    10. Eross, Andrea & McGroarty, Frank & Urquhart, Andrew & Wolfe, Simon, 2019. "The intraday dynamics of bitcoin," Research in International Business and Finance, Elsevier, vol. 49(C), pages 71-81.
    11. Chen, Chun-nan, 2013. "The predictability of opening returns for the returns of the trading day: Evidence from Taiwan futures market," International Review of Economics & Finance, Elsevier, vol. 25(C), pages 272-281.
    12. Hendershott, Terrence & Livdan, Dmitry & Rösch, Dominik, 2020. "Asset pricing: A tale of night and day," Journal of Financial Economics, Elsevier, vol. 138(3), pages 635-662.
    13. Hussain, Syed Mujahid, 2011. "Simultaneous monetary policy announcements and international stock markets response: An intraday analysis," Journal of Banking & Finance, Elsevier, vol. 35(3), pages 752-764, March.
    14. Gordon Tang, 1997. "Weekly pattern in higher moments: An empirical test in Hong Kong stock market," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 21(1), pages 51-59, March.
    15. Köksal, Bülent, 2012. "An Analysis of Intraday Patterns and Liquidity on the Istanbul Stock Exchange," MPRA Paper 35968, University Library of Munich, Germany.
    16. Tim Bollerslev & Jia Li & Yuan Xue, 2018. "Volume, Volatility, and Public News Announcements," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(4), pages 2005-2041.
    17. Steven L. Heston & Robert A. Korajczyk & Ronnie Sadka, 2010. "Intraday Patterns in the Cross‐section of Stock Returns," Journal of Finance, American Finance Association, vol. 65(4), pages 1369-1407, August.
    18. Kim Christensen & Ulrich Hounyo & Zhi Liu, 2024. "A nonparametric test for diurnal variation in spot correlation processes," Papers 2408.02757, arXiv.org.
    19. Jiayi Li & Sumei Luo & Guangyou Zhou, 2021. "Call auction, continuous trading and closing price formation," Quantitative Finance, Taylor & Francis Journals, vol. 21(6), pages 1037-1065, June.
    20. Pascual, Roberto, 1999. "How does liquidity behave? A multidimensional analysis of NYSE stocks," DEE - Working Papers. Business Economics. WB 6433, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.

    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:2409.11339. 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.