IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2407.10561.html
   My bibliography  Save this paper

Nash Equilibrium between Brokers and Traders

Author

Listed:
  • 'Alvaro Cartea
  • Sebastian Jaimungal
  • Leandro S'anchez-Betancourt

Abstract

We study the perfect information Nash equilibrium between a broker and her clients -- an informed trader and an uniformed trader. In our model, the broker trades in the lit exchange where trades have instantaneous and transient price impact with exponential resilience, while both clients trade with the broker. The informed trader and the broker maximise expected wealth subject to inventory penalties, while the uninformed trader is not strategic and sends the broker random buy and sell orders. We characterise the Nash equilibrium of the trading strategies with the solution to a coupled system of forward-backward stochastic differential equations (FBSDEs). We solve this system explicitly and study the effect of information, profitability, and inventory control in the trading strategies of the broker and the informed trader.

Suggested Citation

  • 'Alvaro Cartea & Sebastian Jaimungal & Leandro S'anchez-Betancourt, 2024. "Nash Equilibrium between Brokers and Traders," Papers 2407.10561, arXiv.org, revised Jul 2024.
    • Handle: RePEc:arx:papers:2407.10561
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2407.10561
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sanford J. Grossman & Merton H. Miller, 1988. "Liquidity and Market Structure," NBER Working Papers 2641, National Bureau of Economic Research, Inc.
    2. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    3. 'Alvaro Cartea & Sebastian Jaimungal & Tianyi Jia, 2020. "Trading Foreign Exchange Triplets," Papers 2004.12011, arXiv.org.
    4. repec:bla:jfinan:v:43:y:1988:i:3:p:617-37 is not listed on IDEAS
    5. M. Butz & R. Oomen, 2019. "Internalisation by electronic FX spot dealers," Quantitative Finance, Taylor & Francis Journals, vol. 19(1), pages 35-56, January.
    6. Philippe Casgrain & Sebastian Jaimungal, 2020. "Mean‐field games with differing beliefs for algorithmic trading," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 995-1034, July.
    7. Marcel Nutz & Kevin Webster & Long Zhao, 2023. "Unwinding Stochastic Order Flow: When to Warehouse Trades," Papers 2310.14144, arXiv.org.
    8. repec:hal:wpaper:hal-03941548 is not listed on IDEAS
    9. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    10. Eyal Neuman & Moritz Vo{ss}, 2020. "Optimal Signal-Adaptive Trading with Temporary and Transient Price Impact," Papers 2002.09549, arXiv.org, revised Jan 2022.
    11. Álvaro Cartea & Leandro Sánchez-Betancourt, 2023. "Optimal execution with stochastic delay," Finance and Stochastics, Springer, vol. 27(1), pages 1-47, January.
    12. Albert S. Kyle, 1989. "Informed Speculation with Imperfect Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(3), pages 317-355.
    13. Peter Bank & Ibrahim Ekren & Johannes Muhle-Karbe, 2018. "Liquidity in Competitive Dealer Markets," Papers 1807.08278, arXiv.org, revised Mar 2021.
    14. Peter Bank & Ibrahim Ekren & Johannes Muhle‐Karbe, 2021. "Liquidity in competitive dealer markets," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 827-856, July.
    15. Rama Cont & Alessandro Micheli & Eyal Neuman, 2022. "Fast and Slow Optimal Trading with Exogenous Information," Papers 2210.01901, arXiv.org, revised Jun 2023.
    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. Alexander Barzykin & Robert Boyce & Eyal Neuman, 2024. "Unwinding Toxic Flow with Partial Information," Papers 2407.04510, arXiv.org.
    2. Marcel Nutz & Kevin Webster & Long Zhao, 2023. "Unwinding Stochastic Order Flow: When to Warehouse Trades," Papers 2310.14144, arXiv.org.
    3. Philippe Bergault & Leandro S'anchez-Betancourt, 2024. "A Mean Field Game between Informed Traders and a Broker," Papers 2401.05257, arXiv.org.
    4. 'Alvaro Cartea & Gerardo Duran-Martin & Leandro S'anchez-Betancourt, 2023. "Detecting Toxic Flow," Papers 2312.05827, arXiv.org.
    5. Masamitsu Ohnishi & Makoto Shimoshimizu, 2024. "Trade execution games in a Markovian environment," Papers 2405.07184, arXiv.org.
    6. Peter Bank & Ibrahim Ekren & Johannes Muhle‐Karbe, 2021. "Liquidity in competitive dealer markets," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 827-856, July.
    7. Escribano, Álvaro & Tapia, Mikel & Pascual, Roberto, 1999. "How does liquidity behave? A multidimensional analysis of NYSE stocks," DEE - Working Papers. Business Economics. WB 6433, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    8. Matthew Pritsker, 2005. "Large investors: implications for equilibrium asset, returns, shock absorption, and liquidity," Finance and Economics Discussion Series 2005-36, Board of Governors of the Federal Reserve System (U.S.).
    9. Dimitri Vayanos & Jiang Wang, 2012. "Market Liquidity -- Theory and Empirical Evidence," NBER Working Papers 18251, National Bureau of Economic Research, Inc.
    10. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    11. Phillip Monin, 2014. "Hedging Market Risk in Optimal Liquidation," Working Papers 14-08, Office of Financial Research, US Department of the Treasury.
    12. Ranaldo, Angelo & Somogyi, Fabricius, 2021. "Asymmetric information risk in FX markets," Journal of Financial Economics, Elsevier, vol. 140(2), pages 391-411.
    13. Vayanos, Dimitri & Wang, Jiang, 2013. "Market Liquidity—Theory and Empirical Evidence ," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1289-1361, Elsevier.
    14. Jarrow, Robert & Li, Siguang, 2021. "Endogenous liquidity risk and dealer market structure," The Quarterly Review of Economics and Finance, Elsevier, vol. 81(C), pages 449-453.
    15. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    16. Peter Bank & Ibrahim Ekren & Johannes Muhle-Karbe, 2018. "Liquidity in Competitive Dealer Markets," Papers 1807.08278, arXiv.org, revised Mar 2021.
    17. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    18. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    19. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.
    20. Samuel Cohen & Marc Sabat'e Vidales & David v{S}iv{s}ka & {L}ukasz Szpruch, 2023. "Inefficiency of CFMs: hedging perspective and agent-based simulations," Papers 2302.04345, 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:2407.10561. 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.