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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
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    File URL: http://arxiv.org/pdf/2103.14769
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    References listed on IDEAS

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    1. Thierry Foucault & Sophie Moinas & Erik Theissen, 2007. "Does Anonymity Matter in Electronic Limit Order Markets?," The Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1707-1747, 2007 28.
    2. Guillermo Angeris & Tarun Chitra, 2020. "Improved Price Oracles: Constant Function Market Makers," Papers 2003.10001, arXiv.org, revised Jun 2020.
    3. 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..
    4. Alex Evans, 2020. "Liquidity Provider Returns in Geometric Mean Markets," Papers 2006.08806, arXiv.org, revised Jul 2020.
    5. Guillermo Angeris & Alex Evans & Tarun Chitra, 2020. "When does the tail wag the dog? Curvature and market making," Papers 2012.08040, arXiv.org.
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    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, revised Aug 2023.
    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.

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