IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2305.14604.html
   My bibliography  Save this paper

Automated Market Making and Arbitrage Profits in the Presence of Fees

Author

Listed:
  • Jason Milionis
  • Ciamac C. Moallemi
  • Tim Roughgarden

Abstract

We consider the impact of trading fees on the profits of arbitrageurs trading against an automated marker marker (AMM) or, equivalently, on the adverse selection incurred by liquidity providers due to arbitrage. We extend the model of Milionis et al. [2022] for a general class of two asset AMMs to both introduce fees and discrete Poisson block generation times. In our setting, we are able to compute the expected instantaneous rate of arbitrage profit in closed form. When the fees are low, in the fast block asymptotic regime, the impact of fees takes a particularly simple form: fees simply scale down arbitrage profits by the fraction of time that an arriving arbitrageur finds a profitable trade.

Suggested Citation

  • Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden, 2023. "Automated Market Making and Arbitrage Profits in the Presence of Fees," Papers 2305.14604, arXiv.org.
  • Handle: RePEc:arx:papers:2305.14604
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2305.14604
    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.
    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. 'Alvaro Cartea & Fayc{c}al Drissi & Marcello Monga, 2023. "Decentralised Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision," Papers 2309.08431, arXiv.org, revised Jun 2024.
    2. Matthew Willetts & Christian Harrington, 2024. "Rebalancing-versus-Rebalancing: Improving the fidelity of Loss-versus-Rebalancing," Papers 2410.23404, arXiv.org.
    3. Pablo D. Azar & Adrian Casillas & Maryam Farboodi, 2024. "Information and Market Power in DeFi Intermediation," Staff Reports 1102, Federal Reserve Bank of New York.
    4. Lioba Heimbach & Vabuk Pahari & Eric Schertenleib, 2024. "Non-Atomic Arbitrage in Decentralized Finance," Papers 2401.01622, arXiv.org, revised Apr 2024.
    5. Joseph Najnudel & Shen-Ning Tung & Kazutoshi Yamazaki & Ju-Yi Yen, 2024. "An arbitrage driven price dynamics of Automated Market Makers in the presence of fees," Papers 2401.01526, arXiv.org.
    6. Austin Adams & Benjamin Y Chan & Sarit Markovich & Xin Wan, 2023. "Don't Let MEV Slip: The Costs of Swapping on the Uniswap Protocol," Papers 2309.13648, arXiv.org, revised Apr 2024.
    7. Cheuk Yin Lee & Shen-Ning Tung & Tai-Ho Wang, 2024. "Growth rate of liquidity provider's wealth in G3Ms," Papers 2403.18177, arXiv.org.
    8. Viraj Nadkarni & Sanjeev Kulkarni & Pramod Viswanath, 2024. "Adaptive Curves for Optimally Efficient Market Making," Papers 2406.13794, arXiv.org.
    9. Andrea Canidio & Robin Fritsch, 2023. "Arbitrageurs' profits, LVR, and sandwich attacks: batch trading as an AMM design response," Papers 2307.02074, arXiv.org, revised Feb 2024.
    10. Ciamac C. Moallemi & Dan Robinson, 2024. "Loss-Versus-Fair: Efficiency of Dutch Auctions on Blockchains," Papers 2406.00113, arXiv.org, revised Jul 2024.
    11. Marcello Monga, 2024. "Automated Market Making and Decentralized Finance," Papers 2407.16885, 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. Zhimeng Yang & Ariah Klages-Mundt & Lewis Gudgeon, 2023. "Oracle Counterpoint: Relationships between On-chain and Off-chain Market Data," Papers 2303.16331, arXiv.org, revised Jul 2023.
    2. Matthias Nadler & Felix Bekemeier & Fabian Schar, 2022. "DeFi Risk Transfer: Towards A Fully Decentralized Insurance Protocol," Papers 2212.10308, arXiv.org.
    3. Raphael Auer & Bernhard Haslhofer & Stefan Kitzler & Pietro Saggese & Friedhelm Victor, 2024. "The technology of decentralized finance (DeFi)," Digital Finance, Springer, vol. 6(1), pages 55-95, March.
    4. Maxim Bichuch & Zachary Feinstein, 2022. "Axioms for Automated Market Makers: A Mathematical Framework in FinTech and Decentralized Finance," Papers 2210.01227, arXiv.org, revised Sep 2024.
    5. Dev Churiwala & Bhaskar Krishnamachari, 2022. "QLAMMP: A Q-Learning Agent for Optimizing Fees on Automated Market Making Protocols," Papers 2211.14977, arXiv.org.
    6. 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.
    7. Guillermo Angeris & Alex Evans & Tarun Chitra, 2021. "Replicating Monotonic Payoffs Without Oracles," Papers 2111.13740, arXiv.org.
    8. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant, 2022. "Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions," Papers 2212.00336, arXiv.org, revised Nov 2023.
    9. Tarun Chitra & Alex Evans, 2020. "Why Stake When You Can Borrow?," Papers 2006.11156, arXiv.org.
    10. Tristan Lim, 2022. "Predictive Crypto-Asset Automated Market Making Architecture for Decentralized Finance using Deep Reinforcement Learning," Papers 2211.01346, arXiv.org, revised Jan 2023.
    11. Nassib Boueri, 2021. "G3M Impermanent Loss Dynamics," Papers 2108.06593, arXiv.org, revised Jun 2022.
    12. Peplluis R. Esteva & Andrés El-Fakdi & Alberto Ballesteros-Rodríguez, 2023. "Invoice Discounting Using Kelly Criterion by Automated Market Makers-like Implementations," Mathematics, MDPI, vol. 11(7), pages 1-37, March.
    13. Nicola Cantarutti & Alex Harker & Carter Woetzel, 2023. "Silkswap: An asymmetric automated market maker model for stablecoins," Papers 2302.07822, arXiv.org.
    14. Daniel Kirste & Niclas Kannengie{ss}er & Ricky Lamberty & Ali Sunyaev, 2023. "How Automated Market Makers Approach the Thin Market Problem in Cryptoeconomic Systems," Papers 2309.12818, arXiv.org, revised Sep 2023.
    15. Niccol`o Bardoscia & Alessandro Nodari, 2023. "Liquidity Providers Greeks and Impermanent Gain," Papers 2302.11942, arXiv.org, revised Mar 2023.
    16. Michael Darlin & Nikolaos Papadis & Leandros Tassiulas, 2020. "Optimal Bidding Strategy for Maker Auctions," Papers 2009.07086, arXiv.org, revised May 2021.
    17. Guillermo Angeris & Tarun Chitra & Alex Evans & Matthew Lorig, 2022. "A primer on perpetuals," Papers 2209.03307, arXiv.org.
    18. Johannes Rude Jensen & Mohsen Pourpouneh & Kurt Nielsen & Omri Ross, 2021. "The Homogenous Properties of Automated Market Makers," Papers 2105.02782, arXiv.org.
    19. Makridis, Christos A. & Fröwis, Michael & Sridhar, Kiran & Böhme, Rainer, 2023. "The rise of decentralized cryptocurrency exchanges: Evaluating the role of airdrops and governance tokens," Journal of Corporate Finance, Elsevier, vol. 79(C).
    20. Lo, Yuen & Medda, Francesca, 2020. "Uniswap and the rise of the decentralized exchange," MPRA Paper 103925, University Library of Munich, Germany.

    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:2305.14604. 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.