IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2103.14769.html
   My bibliography  Save this paper

Replicating Market Makers

Author

Listed:
  • Guillermo Angeris
  • Alex Evans
  • Tarun Chitra

Abstract

We present a method for constructing Constant Function Market Makers (CFMMs) whose portfolio value functions match a desired payoff. More specifically, we show that the space of concave, nonnegative, nondecreasing, 1-homogeneous payoff functions and the space of convex CFMMs are equivalent; in other words, every CFMM has a concave, nonnegative, nondecreasing, 1-homogeneous payoff function, and every payoff function with these properties has a corresponding convex CFMM. We demonstrate a simple method for recovering a CFMM trading function that produces this desired payoff. This method uses only basic tools from convex analysis and is intimately related to Fenchel conjugacy. We demonstrate our result by constructing trading functions corresponding to basic payoffs, as well as standard financial derivatives such as options and swaps.

Suggested Citation

  • Guillermo Angeris & Alex Evans & Tarun Chitra, 2021. "Replicating Market Makers," Papers 2103.14769, arXiv.org.
  • Handle: RePEc:arx:papers:2103.14769
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2103.14769
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Guillermo Angeris & Tarun Chitra, 2020. "Improved Price Oracles: Constant Function Market Makers," Papers 2003.10001, arXiv.org, revised Jun 2020.
    2. Thierry Foucault & Sophie Moinas & Erik Theissen, 2007. "Does Anonymity Matter in Electronic Limit Order Markets?," Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1707-1747, 2007 28.
    3. Guillermo Angeris & Alex Evans & Tarun Chitra, 2020. "When does the tail wag the dog? Curvature and market making," Papers 2012.08040, arXiv.org.
    4. Peter P. Carr & Robert A. Jarrow, 2008. "The Stop-Loss Start-Gain Paradox and Option Valuation: A new Decomposition into Intrinsic and Time Value," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 4, pages 61-84, World Scientific Publishing Co. Pte. Ltd..
    5. Alex Evans, 2020. "Liquidity Provider Returns in Geometric Mean Markets," Papers 2006.08806, arXiv.org, revised Jul 2020.
    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. Neelesh Tiruviluamala & Alexander Port & Erik Lewis, 2022. "A General Framework for Impermanent Loss in Automated Market Makers," Papers 2203.11352, arXiv.org.
    2. Maxim Bichuch & Zachary Feinstein, 2022. "Axioms for Automated Market Makers: A Mathematical Framework in FinTech and Decentralized Finance," Papers 2210.01227, arXiv.org.
    3. 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.
    4. Alexander Port & Neelesh Tiruviluamala, 2022. "Mixing Constant Sum and Constant Product Market Makers," Papers 2203.12123, arXiv.org, revised Apr 2022.
    5. Guillermo Angeris & Alex Evans & Tarun Chitra, 2021. "Replicating Monotonic Payoffs Without Oracles," Papers 2111.13740, 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. 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.
    2. Johannes Rude Jensen & Mohsen Pourpouneh & Kurt Nielsen & Omri Ross, 2021. "The Homogenous Properties of Automated Market Makers," Papers 2105.02782, arXiv.org.
    3. 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.
    4. Neelesh Tiruviluamala & Alexander Port & Erik Lewis, 2022. "A General Framework for Impermanent Loss in Automated Market Makers," Papers 2203.11352, arXiv.org.
    5. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden & Anthony Lee Zhang, 2022. "Automated Market Making and Loss-Versus-Rebalancing," Papers 2208.06046, arXiv.org, revised Sep 2022.
    6. Guillermo Angeris & Alex Evans & Tarun Chitra, 2021. "Replicating Monotonic Payoffs Without Oracles," Papers 2111.13740, arXiv.org.
    7. Robin Fritsch & Roger Wattenhofer, 2021. "A Note on Optimal Fees for Constant Function Market Makers," Papers 2105.13510, arXiv.org.
    8. Robin Fritsch, 2021. "Concentrated Liquidity in Automated Market Makers," Papers 2110.01368, arXiv.org.
    9. Guillermo Angeris & Alex Evans & Tarun Chitra, 2020. "When does the tail wag the dog? Curvature and market making," Papers 2012.08040, arXiv.org.
    10. Lioba Heimbach & Eric Schertenleib & Roger Wattenhofer, 2022. "Risks and Returns of Uniswap V3 Liquidity Providers," Papers 2205.08904, arXiv.org, revised Sep 2022.
    11. He, Yinghua & Nielsson, Ulf & Guo, Hong & Yang, Jiong, 2014. "Subscribing to transparency," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 189-206.
    12. Duong, Huu Nhan & Kalev, Petko S., 2013. "Anonymity and order submissions," Pacific-Basin Finance Journal, Elsevier, vol. 25(C), pages 101-118.
    13. Menkhoff, Lukas & Schmeling, Maik, 2010. "Trader see, trader do: How do (small) FX traders react to large counterparties' trades?," Journal of International Money and Finance, Elsevier, vol. 29(7), pages 1283-1302, November.
    14. Phuong Pham, Thu & Joakim Westerholm, P., 2013. "An international trend in market design: Endogenous effects of limit order book transparency on volatility, spreads, depth and volume," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 27(C), pages 202-223.
    15. Dennis, Patrick J. & Sandås, Patrik, 2014. "Does Trading Anonymously Enhance Liquidity?," Working Paper Series 288, Sveriges Riksbank (Central Bank of Sweden).
    16. Gousgounis, Eleni & Onur, Esen, 2018. "The effect of pit closure on futures trading," Journal of Commodity Markets, Elsevier, vol. 10(C), pages 69-90.
    17. Menkhoff, Lukas & Osler, Carol L. & Schmeling, Maik, 2010. "Limit-order submission strategies under asymmetric information," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2665-2677, November.
    18. Ymir Makinen & Juho Kanniainen & Moncef Gabbouj & Alexandros Iosifidis, 2018. "Forecasting of Jump Arrivals in Stock Prices: New Attention-based Network Architecture using Limit Order Book Data," Papers 1810.10845, arXiv.org.
    19. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    20. Lannoo, Karel & Thomadakis, Apostolos, 2020. "Derivatives in Sustainable Finance," ECMI Papers 29791, Centre for European Policy Studies.

    More about this item

    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:2103.14769. See general information about how to correct material in RePEc.

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

    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 hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.