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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 - Ecole Polytechnique - X - École polytechnique - 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

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    1. Olivier Guéant, 2017. "Optimal market making," Post-Print hal-02862554, HAL.
    2. N. Baradel & Bruno Bouchard & N. m. Dang, 2016. "Optimal Trading with Online Parameter Revisions," Post-Print hal-01590602, HAL.
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    6. Rama Cont & Adrien De Larrard, 2012. "Order book dynamics in liquid markets: limit theorems and diffusion approximations," Papers 1202.6412, arXiv.org.
    7. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    8. Frédéric Abergel & Côme Huré & Huyên Pham, 2019. "Algorithmic trading in a microstructural limit order book model," Working Papers hal-01514987, HAL.
    9. 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.
    10. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
    11. 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.
    12. Olivier Guéant, 2017. "Optimal market making," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-02862554, HAL.
    13. Charles-Albert Lehalle & Othmane Mounjid & Mathieu Rosenbaum, 2018. "Optimal liquidity-based trading tactics," Papers 1803.05690, arXiv.org.
    14. 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.
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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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