IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2012.08040.html
   My bibliography  Save this paper

When does the tail wag the dog? Curvature and market making

Author

Listed:
  • Guillermo Angeris
  • Alex Evans
  • Tarun Chitra

Abstract

Liquidity and trading activity on constant function market makers (CFMMs) such as Uniswap, Curve, and Balancer has grown significantly in the second half of 2020. Much of the growth of these protocols has been driven by incentivized pools or 'yield farming', which reward participants in crypto assets for providing liquidity to CFMMs. As a result, CFMMs and associated protocols, which were historically very small markets, now constitute the most liquid trading venues for a large number of crypto assets. But what does it mean for a CFMM to be the most liquid market? In this paper, we propose a basic definition of price sensitivity and liquidity. We show that this definition is tightly related to the curvature of a CFMM's trading function and can be used to explain a number of heuristic results. For example, we show that low-curvature markets are good for coins whose market value is approximately fixed and that high-curvature markets are better for liquidity providers when traders have an informational edge. Additionally, the results can also be used to model interacting markets and explain the rise of incentivized liquidity provision, also known as 'yield farming.'

Suggested Citation

  • Guillermo Angeris & Alex Evans & Tarun Chitra, 2020. "When does the tail wag the dog? Curvature and market making," Papers 2012.08040, arXiv.org.
    • Handle: RePEc:arx:papers:2012.08040
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2012.08040
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2004. "Fluctuations and response in financial markets: the subtle nature of 'random' price changes," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 176-190.
    2. Guillermo Angeris & Tarun Chitra, 2020. "Improved Price Oracles: Constant Function Market Makers," Papers 2003.10001, arXiv.org, revised Jun 2020.
    3. Glosten, Lawrence R. & Milgrom, Paul R., 1985. "Bid, ask and transaction prices in a specialist market with heterogeneously informed traders," Journal of Financial Economics, Elsevier, vol. 14(1), pages 71-100, March.
    4. Glosten, Lawrence R, 1994. "Is the Electronic Open Limit Order Book Inevitable?," Journal of Finance, American Finance Association, vol. 49(4), pages 1127-1161, September.
    5. Enzo Busseti & Ernest K. Ryu & Stephen Boyd, 2016. "Risk-Constrained Kelly Gambling," Papers 1603.06183, arXiv.org.
    6. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    7. Maltritz, Dominik & Eichler, Stefan, 2010. "Currency crisis prediction using ADR market data: An options-based approach," International Journal of Forecasting, Elsevier, vol. 26(4), pages 858-884, October.
    8. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    9. Ismael Lemhadri, 2018. "Market impact in a latent order book," Working Papers hal-01711192, HAL.
    10. Patrick Cheridito & Michael Kupper & Ludovic Tangpi, 2016. "Duality formulas for robust pricing and hedging in discrete time," Papers 1602.06177, arXiv.org, revised Sep 2017.
    11. Robin Hanson, 2003. "Combinatorial Information Market Design," Information Systems Frontiers, Springer, vol. 5(1), pages 107-119, January.
    12. Alex Evans, 2020. "Liquidity Provider Returns in Geometric Mean Markets," Papers 2006.08806, arXiv.org, revised Jul 2020.
    13. Richard K. Lyons & Ganesh Viswanath-Natraj, 2020. "What Keeps Stablecoins Stable?," NBER Working Papers 27136, National Bureau of Economic Research, Inc.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Guéant, 2024. "Automated market makers: mean-variance analysis of LPs payoffs and design of pricing functions," Digital Finance, Springer, vol. 6(2), pages 225-247, June.
    2. Sam M. Werner & Daniel Perez & Lewis Gudgeon & Ariah Klages-Mundt & Dominik Harz & William J. Knottenbelt, 2021. "SoK: Decentralized Finance (DeFi)," Papers 2101.08778, arXiv.org, revised Sep 2022.
    3. Ariah Klages-Mundt & Steffen Schuldenzucker, 2022. "Designing Autonomous Markets for Stablecoin Monetary Policy," Papers 2212.12398, arXiv.org.
    4. Robin Fritsch & Roger Wattenhofer, 2021. "A Note on Optimal Fees for Constant Function Market Makers," Papers 2105.13510, arXiv.org.
    5. de Andrés, Pablo & Arroyo, David & Correia, Ricardo & Rezola, Alvaro, 2022. "Challenges of the market for initial coin offerings," International Review of Financial Analysis, Elsevier, vol. 79(C).
    6. Neelesh Tiruviluamala & Alexander Port & Erik Lewis, 2022. "A General Framework for Impermanent Loss in Automated Market Makers," Papers 2203.11352, arXiv.org.
    7. Guillermo Angeris & Akshay Agrawal & Alex Evans & Tarun Chitra & Stephen Boyd, 2021. "Constant Function Market Makers: Multi-Asset Trades via Convex Optimization," Papers 2107.12484, arXiv.org.
    8. Johannes Rude Jensen & Mohsen Pourpouneh & Kurt Nielsen & Omri Ross, 2021. "The Homogenous Properties of Automated Market Makers," Papers 2105.02782, arXiv.org.
    9. Tobias Bitterli & Fabian Schar, 2023. "Decentralized Exchanges: The Profitability Frontier of Constant Product Market Makers," Papers 2302.05219, arXiv.org, revised Mar 2023.
    10. Guillermo Angeris & Alex Evans & Tarun Chitra, 2021. "Replicating Market Makers," Papers 2103.14769, arXiv.org.
    11. Robin Fritsch, 2021. "Concentrated Liquidity in Automated Market Makers," Papers 2110.01368, arXiv.org.

    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. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    2. Thibault Jaisson, 2014. "Market impact as anticipation of the order flow imbalance," Papers 1402.1288, arXiv.org.
    3. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Henri Waelbroeck, 2013. "How efficiency shapes market impact," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1743-1758, November.
    4. Steffen Bohn, 2011. "The slippage paradox," Working Papers hal-00574268, HAL.
    5. Johannes Rude Jensen & Mohsen Pourpouneh & Kurt Nielsen & Omri Ross, 2021. "The Homogenous Properties of Automated Market Makers," Papers 2105.02782, arXiv.org.
    6. Michele Vodret & Iacopo Mastromatteo & Bence T'oth & Michael Benzaquen, 2021. "Do fundamentals shape the price response? A critical assessment of linear impact models," Papers 2112.04245, arXiv.org.
    7. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    8. Michele Vodret & Bence Tóth & Iacopo Mastromatteo & Michael Benzaquen, 2022. "Do fundamentals shape the price response? A critical assessment of linear impact models," Post-Print hal-03797375, HAL.
    9. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    10. Steffen Bohn, 2011. "The slippage paradox," Papers 1103.2214, arXiv.org.
    11. Chang, Sanders S. & Wang, F. Albert, 2015. "Adverse selection and the presence of informed trading," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 19-33.
    12. Baruch, Shmuel & Panayides, Marios & Venkataraman, Kumar, 2017. "Informed trading and price discovery before corporate events," Journal of Financial Economics, Elsevier, vol. 125(3), pages 561-588.
    13. Bondarenko, Oleg, 2001. "Competing market makers, liquidity provision, and bid-ask spreads," Journal of Financial Markets, Elsevier, vol. 4(3), pages 269-308, June.
    14. Chakravarty, Sugato & Harris, Fredreck H. deB. & Wood, Roger A., 2001. "Do Bid-Ask Spreads or Bid and Ask Depths Convey New Information First?," Purdue University Economics Working Papers 1149, Purdue University, Department of Economics.
    15. Peter Gomber & Satchit Sagade & Erik Theissen & Moritz Christian Weber & Christian Westheide, 2017. "Competition Between Equity Markets: A Review Of The Consolidation Versus Fragmentation Debate," Journal of Economic Surveys, Wiley Blackwell, vol. 31(3), pages 792-814, July.
    16. Lee, Yi-Tsung & Liu, Yu-Jane & Roll, Richard & Subrahmanyam, Avanidhar, 2001. "Order Imbalances and Market Efficiency: Evidence from the Taiwan Stock Exchange, Forthcoming in the Journal of Financial and Quantitative Analysis," University of California at Los Angeles, Anderson Graduate School of Management qt7w8106qn, Anderson Graduate School of Management, UCLA.
    17. PASCUAL, Roberto & VEREDAS, David, 2006. "Does the open limit order book matter in explaining long run volatility ?," LIDAM Discussion Papers CORE 2006110, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. G. Wuyts, 2007. "Stock Market Liquidity.Determinants and Implications," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(2), pages 279-316.
    19. Rubio, Gonzalo & Tapia, Mikel, 1996. "The liquidity premiun in equity pricing under a continuous auction system," DEE - Working Papers. Business Economics. WB 7014, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    20. Malinova, Katya & Park, Andreas, 2013. "Liquidity, volume and price efficiency: The impact of order vs. quote driven trading," Journal of Financial Markets, Elsevier, vol. 16(1), pages 104-126.

    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:2012.08040. 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.