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

Author

Listed:
  • Aurélien Alfonsi

    () (Université Paris-Est, CERMICS)

  • Pierre Blanc

    () (Université Paris-Est, CERMICS)

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.

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:d:10.1007_s00780-015-0282-y
    DOI: 10.1007/s00780-015-0282-y
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Working Papers hal-02998555, HAL.
    2. Joffrey Derchu, 2020. "A Bayesian perspective on the microstructure of the price formation process," Papers 2012.15705, arXiv.org.
    3. Paul Jusselin, 2020. "Optimal market making with persistent order flow," Papers 2003.05958, arXiv.org, revised Oct 2020.
    4. 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.
    5. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2020. "Portfolio Liquidation Games with Self-Exciting Order Flow," Papers 2011.05589, arXiv.org.
    6. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2017. "Hybrid marked point processes: characterisation, existence and uniqueness," Papers 1707.06970, arXiv.org, revised Oct 2018.
    7. Ingemar Kaj & Mine Caglar, 2017. "A buffer Hawkes process for limit order books," Papers 1710.03506, arXiv.org.
    8. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Papers 2005.05730, arXiv.org.
    9. Hadrien De March & Charles-Albert Lehalle, 2018. "Optimal trading using signals," Papers 1811.03718, 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;
    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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