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Optimal inventory management and order book modeling

Author

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  • Nicolas Baradel

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, ENSAE - Ecole Nationale de la Statistique et de l'Analyse Economique - Ecole Nationale de la Statistique et de l'Analyse Economique)

  • Bruno Bouchard

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, PSL - Université Paris Sciences et Lettres)

  • David Evangelista

    (KAUST - King Abdullah University of Science and Technology [Saudi Arabia])

  • Othmane Mounjid

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

We model the behavior of three agent classes acting dynamically in a limit order book of a financial asset. Namely, we consider market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB). Given a prior dynamic of the order book, similar to the one considered in the Queue-Reactive models [14, 20, 21], the MM and the HFT define their trading strategy by optimizing the expected utility of terminal wealth, while the IB has a prescheduled task to sell or buy many shares of the considered asset. We derive the variational partial differential equations that characterize the value functions of the MM and HFT and explain how almost optimal control can be deduced from them. We then provide a first illustration of the interactions that can take place between these different market participants by simulating the dynamic of an order book in which each of them plays his own (optimal) strategy.

Suggested Citation

  • Nicolas Baradel & Bruno Bouchard & David Evangelista & Othmane Mounjid, 2019. "Optimal inventory management and order book modeling," Post-Print hal-01710301, HAL.
    • Handle: RePEc:hal:journl:hal-01710301
    Note: View the original document on HAL open archive server: https://hal.science/hal-01710301v2
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    References listed on IDEAS

    as
    1. Foucault, Thierry, 1998. "Order Flow Composition and Trading Costs in Dynamic Limit Order Markets," CEPR Discussion Papers 1817, C.E.P.R. Discussion Papers.
    2. Frédéric Abergel & Côme Huré & Huyên Pham, 2019. "Algorithmic trading in a microstructural limit order book model," Working Papers hal-01514987, HAL.
    3. Fr'ed'eric Abergel & C^ome Hur'e & Huy^en Pham, 2017. "Algorithmic trading in a microstructural limit order book model," Papers 1705.01446, arXiv.org, revised Feb 2020.
    4. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
    5. Olivier Guéant, 2017. "Optimal market making," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(2), pages 112-154, March.
    6. N. Baradel & Bruno Bouchard & N. m. Dang, 2016. "Optimal Trading with Online Parameter Revisions," Post-Print hal-01590602, HAL.
    7. Eric Smith & J Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2003. "Statistical theory of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 481-514.
    8. Parlour, Christine A, 1998. "Price Dynamics in Limit Order Markets," The Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 789-816.
    9. Fabien Guilbaud & Huyên Pham, 2013. "Optimal high-frequency trading with limit and market orders," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 79-94, January.
    10. Rama Cont & Adrien De Larrard, 2012. "Order book dynamics in liquid markets: limit theorems and diffusion approximations," Papers 1202.6412, arXiv.org.
    11. Charles-Albert Lehalle & Othmane Mounjid & Mathieu Rosenbaum, 2018. "Optimal liquidity-based trading tactics," Papers 1803.05690, arXiv.org.
    12. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    13. Weibing Huang & Charles-Albert Lehalle & Mathieu Rosenbaum, 2015. "Simulating and Analyzing Order Book Data: The Queue-Reactive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 107-122, March.
    14. Frédéric Abergel & Aymen Jedidi, 2013. "A Mathematical Approach To Order Book Modeling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1-40.
    15. Foucault, Thierry, 1999. "Order flow composition and trading costs in a dynamic limit order market1," Journal of Financial Markets, Elsevier, vol. 2(2), pages 99-134, May.
    16. Frédéric Abergel & Aymen Jedidi, 2013. "A Mathematical Approach to Order Book Modelling," Post-Print hal-00621253, HAL.
    17. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.
    18. Frederic Abergel & Aymen Jedidi, 2010. "A Mathematical Approach to Order Book Modeling," Papers 1010.5136, arXiv.org, revised Mar 2013.
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    Cited by:

    1. Lester Ingber, 2020. "Developing Bid-Ask Probabilities for High-Frequency Trading," Virtual Economics, The London Academy of Science and Business, vol. 3(2), pages 7-24, April.

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    Keywords

    Optimal control; Optimal trading; market impact;
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