IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2205.00494.html
   My bibliography  Save this paper

Transient impact from the Nash equilibrium of a permanent market impact game

Author

Listed:
  • Francesco Cordoni
  • Fabrizio Lillo

Abstract

A large body of empirical literature has shown that market impact of financial prices is transient. However, from a theoretical standpoint, the origin of this temporary nature is still unclear. We show that an implied transient impact arises from the Nash equilibrium between a directional trader and one arbitrageur in a market impact game with fixed and permanent impact. The implied impact is the one that can be empirically inferred from the directional trader's trading profile and price reaction to order flow. Specifically, we propose two approaches to derive the functional form of the decay kernel of the Transient Impact Model, one of the most popular empirical models for transient impact, from the behaviour of the directional trader at the Nash equilibrium. The first is based on the relationship between past order flow and future price change, while in the second we solve an inverse optimal execution problem. We show that in the first approach the implied kernel is unique, while in the second case infinite solutions exist and a linear kernel can always be inferred.

Suggested Citation

  • Francesco Cordoni & Fabrizio Lillo, 2022. "Transient impact from the Nash equilibrium of a permanent market impact game," Papers 2205.00494, arXiv.org, revised Mar 2023.
    • Handle: RePEc:arx:papers:2205.00494
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2205.00494
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michele Vodret & Iacopo Mastromatteo & Bence T'oth & Michael Benzaquen, 2020. "A Stationary Kyle Setup: Microfounding propagator models," Papers 2011.10242, arXiv.org, revised Feb 2021.
    2. Alexander Schied & Tao Zhang, 2019. "A Market Impact Game Under Transient Price Impact," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 102-121, February.
    3. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2004. "Fluctuations and response in financial markets: the subtle nature of 'random' price changes," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 176-190.
    4. Alexander Schied & Elias Strehle & Tao Zhang, 2015. "High-frequency limit of Nash equilibria in a market impact game with transient price impact," Papers 1509.08281, arXiv.org, revised May 2017.
    5. Michele Vodret & Iacopo Mastromatteo & Bence Tóth & Michael Benzaquen, 2021. "A Stationary Kyle Setup: Microfounding propagator models," Post-Print hal-03016486, HAL.
    6. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Henri Waelbroeck, 2013. "How efficiency shapes market impact," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1743-1758, November.
    7. Damian Eduardo Taranto & Giacomo Bormetti & Jean-Philippe Bouchaud & Fabrizio Lillo & Bence Tóth, 2018. "Linear models for the impact of order flow on prices. II. The Mixture Transition Distribution model," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 917-931, June.
    8. Bruce Ian Carlin & Miguel Sousa Lobo & S. Viswanathan, 2007. "Episodic Liquidity Crises: Cooperative and Predatory Trading," Journal of Finance, American Finance Association, vol. 62(5), pages 2235-2274, October.
    9. Damian Eduardo Taranto & Giacomo Bormetti & Jean-Philippe Bouchaud & Fabrizio Lillo & Bence Tóth, 2018. "Linear models for the impact of order flow on prices. I. History dependent impact models," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 903-915, June.
    10. J. Donier & J. Bonart & I. Mastromatteo & J.-P. Bouchaud, 2015. "A fully consistent, minimal model for non-linear market impact," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1109-1121, July.
    11. Jonathan Donier & Julius Bonart & Iacopo Mastromatteo & Jean-Philippe Bouchaud, 2014. "A fully consistent, minimal model for non-linear market impact," Papers 1412.0141, arXiv.org, revised Mar 2015.
    Full references (including those not matched with items on IDEAS)

    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. Fabrizio Lillo, 2021. "Order flow and price formation," Papers 2105.00521, arXiv.org.
    2. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    3. Fr'ed'eric Bucci & Michael Benzaquen & Fabrizio Lillo & Jean-Philippe Bouchaud, 2019. "Slow decay of impact in equity markets: insights from the ANcerno database," Papers 1901.05332, arXiv.org, revised Jan 2019.
    4. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2022. "Portfolio liquidation games with self‐exciting order flow," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1020-1065, October.
    5. Louis Saddier & Matteo Marsili, 2023. "A Bayesian theory of market impact," Papers 2303.08867, arXiv.org, revised May 2024.
    6. Frédéric Bucci & Michael Benzaquen & Fabrizio Lillo & Jean-Philippe Bouchaud, 2019. "Slow Decay of Impact in Equity Markets: Insights from the ANcerno Database," Post-Print hal-02323357, HAL.
    7. Moritz Voß, 2022. "A two-player portfolio tracking game," Mathematics and Financial Economics, Springer, volume 16, number 6, March.
    8. Michele Vodret & Bence Tóth & Iacopo Mastromatteo & Michael Benzaquen, 2022. "Do fundamentals shape the price response? A critical assessment of linear impact models," Post-Print hal-03797375, HAL.
    9. Emilio Said, 2022. "Market Impact: Empirical Evidence, Theory and Practice," Working Papers hal-03668669, HAL.
    10. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2020. "Portfolio Liquidation Games with Self-Exciting Order Flow," Papers 2011.05589, arXiv.org.
    11. Francesco Cordoni & Fabrizio Lillo, 2020. "Instabilities in Multi-Asset and Multi-Agent Market Impact Games," Papers 2004.03546, arXiv.org, revised Nov 2021.
    12. Alexander Schied & Tao Zhang, 2019. "A Market Impact Game Under Transient Price Impact," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 102-121, February.
    13. Jean-Philippe Bouchaud, 2021. "The Inelastic Market Hypothesis: A Microstructural Interpretation," Papers 2108.00242, arXiv.org, revised Jan 2022.
    14. Moritz Vo{ss}, 2019. "A two-player portfolio tracking game," Papers 1911.05122, arXiv.org, revised Jul 2022.
    15. Fu, Guanxing & Horst, Ulrich & Xia, Xiaonyu, 2022. "Portfolio Liquidation Games with Self-Exciting Order Flow," Rationality and Competition Discussion Paper Series 327, CRC TRR 190 Rationality and Competition.
    16. Brunovský, Pavol & Černý, Aleš & Komadel, Ján, 2018. "Optimal trade execution under endogenous pressure to liquidate: Theory and numerical solutions," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1159-1171.
    17. Damian Eduardo Taranto & Giacomo Bormetti & Jean-Philippe Bouchaud & Fabrizio Lillo & Bence Toth, 2016. "Linear models for the impact of order flow on prices II. The Mixture Transition Distribution model," Papers 1604.07556, arXiv.org.
    18. Sergey Nadtochiy, 2020. "A simple microstructural explanation of the concavity of price impact," Papers 2001.01860, arXiv.org, revised Dec 2020.
    19. Michele Vodret & Iacopo Mastromatteo & Bence T'oth & Michael Benzaquen, 2021. "Do fundamentals shape the price response? A critical assessment of linear impact models," Papers 2112.04245, arXiv.org.
    20. Zoltan Eisler & Jean-Philippe Bouchaud, 2016. "Price impact without order book: A study of the OTC credit index market," Papers 1609.04620, 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:2205.00494. 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.