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Dynamic optimal execution in a mixed-market-impact Hawkes price model

Author

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  • Aurélien Alfonsi

    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTech, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École des Ponts ParisTech - Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique)

  • Pierre Blanc

    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École des Ponts ParisTech, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École des Ponts ParisTech - Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique)

Abstract

We study a linear price impact model including other liquidity takers, whose flow of orders either follows a Poisson or a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-formula optimal strategy describes in particular how one should react to the orders of other traders. This result enables us to discuss the viability of the market. It is shown that Poissonian arrivals of orders lead to quite robust Price Manipulation Strategies in the sense of Huberman and Stanzl. Instead, a particular set of conditions on the Hawkes model balances the self-excitation of the order flow with the resilience of the price, excludes Price Manipulation Strategies and gives some market stability.

Suggested Citation

  • Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Post-Print hal-00971369, HAL.
    • Handle: RePEc:hal:journl:hal-00971369
    DOI: 10.1007/s00780-015-0282-y
    Note: View the original document on HAL open archive server: https://enpc.hal.science/hal-00971369v2
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. A. Papanicolaou & H. Fu & P. Krishnamurthy & B. Healy & F. Khorrami, 2023. "An Optimal Control Strategy for Execution of Large Stock Orders Using LSTMs," Papers 2301.09705, arXiv.org, revised Jun 2023.
    2. Dupret, Jean-Loup & Hainaut, Donatien, 2023. "Optimal liquidation under indirect price impact with propagator," LIDAM Discussion Papers ISBA 2023012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Simon Clinet & Jean-Franc{c}ois Perreton & Serge Reydellet, 2021. "Optimal trading: a model predictive control approach," Papers 2110.11008, arXiv.org, revised Nov 2021.
    4. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Working Papers hal-02998555, HAL.
    5. Joffrey Derchu, 2020. "A Bayesian viewpoint on the price formation process," Papers 2012.15705, arXiv.org, revised Sep 2021.
    6. Da Fonseca, José & Malevergne, Yannick, 2021. "A simple microstructure model based on the Cox-BESQ process with application to optimal execution policy," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    7. Borland, Lisa, 2016. "Exploring the dynamics of financial markets: from stock prices to strategy returns," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 59-74.
    8. 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.
    9. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    10. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.
    11. Paul Jusselin, 2020. "Optimal market making with persistent order flow," Papers 2003.05958, arXiv.org, revised Oct 2020.
    12. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2022. "A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies," Papers 2207.00446, arXiv.org, revised Sep 2023.
    13. Thibaut Mastrolia & Tianrui Xu, 2024. "Clearing time randomization and transaction fees for auction market design," Papers 2405.09764, arXiv.org, revised Oct 2024.
    14. José Da Fonseca & Riadh Zaatour, 2017. "Correlation and Lead–Lag Relationships in a Hawkes Microstructure Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(3), pages 260-285, March.
    15. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2020. "Portfolio Liquidation Games with Self-Exciting Order Flow," Papers 2011.05589, arXiv.org.
    16. Hadrien De March & Charles-Albert Lehalle, 2018. "Optimal trading using signals," Papers 1811.03718, arXiv.org.
    17. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2017. "Hybrid marked point processes: characterisation, existence and uniqueness," Papers 1707.06970, arXiv.org, revised Oct 2018.
    18. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2021. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Post-Print hal-02998555, HAL.
    19. Ingemar Kaj & Mine Caglar, 2017. "A buffer Hawkes process for limit order books," Papers 1710.03506, arXiv.org.
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