IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2401.01526.html
   My bibliography  Save this paper

An arbitrage driven price dynamics of Automated Market Makers in the presence of fees

Author

Listed:
  • Joseph Najnudel
  • Shen-Ning Tung
  • Kazutoshi Yamazaki
  • Ju-Yi Yen

Abstract

We present a model for price dynamics in the Automated Market Makers (AMM) setting. Within this framework, we propose a reference market price following a geometric Brownian motion. The AMM price is constrained by upper and lower bounds, determined by constant multiplications of the reference price. Through the utilization of local times and excursion-theoretic approaches, we derive several analytical results, including its time-changed representation and limiting behavior.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2401.01526
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2401.01526
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden, 2023. "Automated Market Making and Arbitrage Profits in the Presence of Fees," Papers 2305.14604, arXiv.org.
    2. Agostino Capponi & Ruizhe Jia, 2021. "The Adoption of Blockchain-based Decentralized Exchanges," Papers 2103.08842, arXiv.org, revised Jul 2021.
    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. Wei-Ru Chen & A. Christian Silva & Shen-Ning Tung, 2024. "Stylized facts in Web3," Papers 2408.07653, arXiv.org, revised Dec 2024.

    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. 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.
    2. Marcello Monga, 2024. "Automated Market Making and Decentralized Finance," Papers 2407.16885, arXiv.org.
    3. Cheuk Yin Lee & Shen-Ning Tung & Tai-Ho Wang, 2024. "Growth rate of liquidity provider's wealth in G3Ms," Papers 2403.18177, arXiv.org.
    4. Annetta Ho & Cosmin Cazan & Andrew Schrumm, 2024. "The Ecology of Automated Market Makers," Discussion Papers 2024-12, Bank of Canada.
    5. 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.
    6. 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.
    7. Chemaya, Nir & Liu, Dingyue, 2024. "The suitability of using Uniswap V2 model to analyze V3 data," Finance Research Letters, Elsevier, vol. 59(C).
    8. Alfred Lehar & Christine Parlour & Marius Zoican, 2023. "Fragmentation and optimal liquidity supply on decentralized exchanges," Papers 2307.13772, arXiv.org, revised May 2024.
    9. Jonathan Chiu & Charles M. Kahn & Thorsten V. Koeppl, 2022. "Grasping decentralized finance through the lens of economic theory," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 55(4), pages 1702-1728, November.
    10. 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.
    11. Marcin Wk{a}torek & Marcin Kr'olczyk & Jaros{l}aw Kwapie'n & Tomasz Stanisz & Stanis{l}aw Dro.zd.z, 2024. "Approaching multifractal complexity in decentralized cryptocurrency trading," Papers 2411.05951, arXiv.org.
    12. Nikolaus Hautsch & Christoph Scheu & Stefan Voigt, 2024. "Building trust takes time: limits to arbitrage for blockchain-based assets," Review of Finance, European Finance Association, vol. 28(4), pages 1345-1381.
    13. Brolley, Michael & Zoican, Marius, 2023. "On-demand fast trading on decentralized exchanges," Finance Research Letters, Elsevier, vol. 51(C).
    14. Andrea Canidio, 2023. "Auctions with Tokens: Monetary Policy as a Mechanism Design Choice," Papers 2301.13794, arXiv.org, revised Aug 2023.
    15. '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.
    16. Ariah Klages-Mundt & Steffen Schuldenzucker, 2022. "Designing Autonomous Markets for Stablecoin Monetary Policy," Papers 2212.12398, arXiv.org.
    17. Basile Caparros & Amit Chaudhary & Olga Klein, 2023. "Blockchain scaling and liquidity concentration on decentralized exchanges," Papers 2306.17742, arXiv.org, revised Mar 2024.
    18. Andrea Barbon & Angelo Ranaldo, 2021. "On The Quality Of Cryptocurrency Markets: Centralized Versus Decentralized Exchanges," Papers 2112.07386, arXiv.org, revised Sep 2024.
    19. Austin Adams, 2024. "Layer 2 be or Layer not 2 be: Scaling on Uniswap v3," Papers 2403.09494, arXiv.org, revised Mar 2024.
    20. Viraj Nadkarni & Sanjeev Kulkarni & Pramod Viswanath, 2024. "Adaptive Curves for Optimally Efficient Market Making," Papers 2406.13794, arXiv.org.

    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:2401.01526. 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.