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

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  • Aurélien Alfonsi
  • Pierre Blanc

Abstract

We study a linear price impact model, including other liquidity takers, whose flow of orders is driven by a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-form 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 (Econometrica, 72:1247–1275, 2004 ). 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. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    • Handle: RePEc:spr:finsto:v:20:y:2016:i:1:p:183-218
    DOI: 10.1007/s00780-015-0282-y
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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. Ying Chen & Ulrich Horst & Hoang Hai Tran, 2019. "Portfolio liquidation under transient price impact -- theoretical solution and implementation with 100 NASDAQ stocks," Papers 1912.06426, arXiv.org.
    10. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    11. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.
    12. Paul Jusselin, 2020. "Optimal market making with persistent order flow," Papers 2003.05958, arXiv.org, revised Oct 2020.
    13. 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.
    14. Thibaut Mastrolia & Tianrui Xu, 2024. "Clearing time randomization and transaction fees for auction market design," Papers 2405.09764, arXiv.org, revised Oct 2024.
    15. 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.
    16. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2020. "Portfolio Liquidation Games with Self-Exciting Order Flow," Papers 2011.05589, arXiv.org.
    17. Hadrien De March & Charles-Albert Lehalle, 2018. "Optimal trading using signals," Papers 1811.03718, arXiv.org.
    18. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2017. "Hybrid marked point processes: characterisation, existence and uniqueness," Papers 1707.06970, arXiv.org, revised Oct 2018.
    19. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2021. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Post-Print hal-02998555, HAL.
    20. Peter Bank & 'Alvaro Cartea & Laura Korber, 2023. "Optimal execution and speculation with trade signals," Papers 2306.00621, arXiv.org, revised Jul 2023.
    21. Ingemar Kaj & Mine Caglar, 2017. "A buffer Hawkes process for limit order books," Papers 1710.03506, arXiv.org.
    22. Tao Chen & Mike Ludkovski & Moritz Vo{ss}, 2022. "On Parametric Optimal Execution and Machine Learning Surrogates," Papers 2204.08581, arXiv.org, revised Oct 2023.
    23. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Papers 2005.05730, arXiv.org.

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    More about this item

    Keywords

    Market impact model; Optimal execution; Hawkes processes; Market microstructure; High-frequency trading; Price manipulations; 91G99; 91B24; 91B26; 60G55; 49J15; C02; C61; C62; G11;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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