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Replicating market makers

Author

Listed:
  • Guillermo Angeris

    (Bain Capital Crypto)

  • Alex Evans

    (Bain Capital Crypto)

  • Tarun Chitra

    (Gauntlet Networks)

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, 2023. "Replicating market makers," Digital Finance, Springer, vol. 5(2), pages 367-387, June.
    • Handle: RePEc:spr:digfin:v:5:y:2023:i:2:d:10.1007_s42521-023-00082-0
    DOI: 10.1007/s42521-023-00082-0
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    References listed on IDEAS

    as
    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 & Akshay Agrawal & Alex Evans & Tarun Chitra & Stephen Boyd, 2022. "Constant Function Market Makers: Multi-asset Trades via Convex Optimization," Springer Optimization and Its Applications, in: Duc A. Tran & My T. Thai & Bhaskar Krishnamachari (ed.), Handbook on Blockchain, pages 415-444, Springer.
    3. Guillermo Angeris & Tarun Chitra, 2020. "Improved Price Oracles: Constant Function Market Makers," Papers 2003.10001, arXiv.org, revised Jun 2020.
    4. Estelle Sterrett & Waylon Jepsen & Evan Kim, 2022. "Replicating Portfolios: Constructing Permissionless Derivatives," Papers 2205.09890, arXiv.org, revised Jun 2022.
    5. Guillermo Angeris & Hsien-Tang Kao & Rei Chiang & Charlie Noyes & Tarun Chitra, 2019. "An analysis of Uniswap markets," Papers 1911.03380, arXiv.org, revised Feb 2021.
    6. Alex Evans & Guillermo Angeris & Tarun Chitra, 2021. "Optimal Fees for Geometric Mean Market Makers," Papers 2104.00446, arXiv.org.
    7. 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..
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Constant function market makers; Decentralized finance; Convex optimization; Fenchel conjugacy;
    All these keywords.

    JEL classification:

    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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