IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00971369.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://enpc.hal.science/hal-00971369v2/document
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s00780-015-0282-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Stephen J. Hardiman & Nicolas Bercot & Jean-Philippe Bouchaud, 2013. "Critical reflexivity in financial markets: a Hawkes process analysis," Papers 1302.1405, arXiv.org, revised Jun 2013.
    2. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2004. "Fluctuations and response in financial markets: the subtle nature of 'random' price changes," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 176-190.
    3. E. Bacry & J. F Muzy, 2013. "Hawkes model for price and trades high-frequency dynamics," Papers 1301.1135, arXiv.org.
    4. Bacry, E. & Delattre, S. & Hoffmann, M. & Muzy, J.F., 2013. "Some limit theorems for Hawkes processes and application to financial statistics," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2475-2499.
    5. Jim Gatheral, 2010. "No-dynamic-arbitrage and market impact," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 749-759.
    6. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
    7. Christian Y. Robert & Mathieu Rosenbaum, 2011. "A New Approach for the Dynamics of Ultra-High-Frequency Data: The Model with Uncertainty Zones," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 344-366, Spring.
    8. Jonathan Donier, 2012. "Market Impact with Autocorrelated Order Flow under Perfect Competition," Papers 1212.4770, arXiv.org.
    9. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    10. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, July.
    11. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    12. Vladimir Filimonov & Didier Sornette, 2012. "Quantifying reflexivity in financial markets: towards a prediction of flash crashes," Papers 1201.3572, arXiv.org, revised Apr 2012.
    13. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    14. Stephen Hardiman & Nicolas Bercot & Jean-Philippe Bouchaud, 2013. "Critical reflexivity in financial markets: a Hawkes process analysis," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(10), pages 1-9, October.
    15. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    16. 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.
    17. Zoltán Eisler & Jean-Philippe Bouchaud & Julien Kockelkoren, 2012. "The price impact of order book events: market orders, limit orders and cancellations," Quantitative Finance, Taylor & Francis Journals, vol. 12(9), pages 1395-1419, September.
    18. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Post-Print hal-01313995, HAL.
    19. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Henri Waelbroeck, 2013. "How efficiency shapes market impact," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1743-1758, November.
    20. Aur'elien Alfonsi & Alexander Schied, 2012. "Capacitary measures for completely monotone kernels via singular control," Papers 1201.2756, arXiv.org, revised Feb 2013.
    21. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    22. Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 133-140.
    23. Erhan Bayraktar & Mike Ludkovski, 2009. "Optimal Trade Execution in Illiquid Markets," Papers 0902.2516, arXiv.org.
    24. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Some limit theorems for Hawkes processes and application to financial statistics," Post-Print hal-01313994, HAL.
    25. Aurélien Alfonsi & Alexander Schied, 2013. "Capacitary measures for completely monotone kernels via singular control," Post-Print hal-00659421, HAL.
    26. A. Gareche & G. Disdier & J. Kockelkoren & J. -P. Bouchaud, 2013. "A Fokker-Planck description for the queue dynamics of large tick stocks," Papers 1304.6819, arXiv.org.
    27. Frédéric Abergel & Aymen Jedidi, 2013. "A Mathematical Approach to Order Book Modelling," Post-Print hal-00621253, HAL.
    28. Frederic Abergel & Aymen Jedidi, 2010. "A Mathematical Approach to Order Book Modeling," Papers 1010.5136, arXiv.org, revised Mar 2013.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. Thibaut Mastrolia & Tianrui Xu, 2024. "Clearing time randomization and transaction fees for auction market design," Papers 2405.09764, arXiv.org, revised Oct 2024.
    5. 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.
    6. Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2020. "Portfolio Liquidation Games with Self-Exciting Order Flow," Papers 2011.05589, arXiv.org.
    7. Hadrien De March & Charles-Albert Lehalle, 2018. "Optimal trading using signals," Papers 1811.03718, arXiv.org.
    8. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2017. "Hybrid marked point processes: characterisation, existence and uniqueness," Papers 1707.06970, arXiv.org, revised Oct 2018.
    9. 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.
    10. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Working Papers hal-02998555, HAL.
    11. Joffrey Derchu, 2020. "A Bayesian viewpoint on the price formation process," Papers 2012.15705, arXiv.org, revised Sep 2021.
    12. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2021. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Post-Print hal-02998555, HAL.
    13. 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).
    14. 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.
    15. 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.
    16. Ingemar Kaj & Mine Caglar, 2017. "A buffer Hawkes process for limit order books," Papers 1710.03506, arXiv.org.
    17. Sadoghi, Amirhossein & Vecer, Jan, 2022. "Optimal liquidation problem in illiquid markets," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1050-1066.
    18. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events," Papers 2005.05730, arXiv.org.
    19. Amirhossein Sadoghi & Jan Vecer, 2022. "Optimal liquidation problem in illiquid markets," Post-Print hal-03696768, HAL.
    20. Paul Jusselin, 2020. "Optimal market making with persistent order flow," Papers 2003.05958, arXiv.org, revised Oct 2020.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Aur'elien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Papers 1404.0648, arXiv.org, revised Jun 2015.
    3. 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.
    4. 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).
    5. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    6. Aur'elien Alfonsi & Pierre Blanc, 2015. "Extension and calibration of a Hawkes-based optimal execution model," Papers 1506.08740, arXiv.org.
    7. Thibault Jaisson, 2014. "Market impact as anticipation of the order flow imbalance," Papers 1402.1288, arXiv.org.
    8. Thibault Jaisson, 2015. "Market impact as anticipation of the order flow imbalance," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1123-1135, July.
    9. Emmanuel Bacry & Thibault Jaisson & Jean-Francois Muzy, 2014. "Estimation of slowly decreasing Hawkes kernels: Application to high frequency order book modelling," Papers 1412.7096, arXiv.org.
    10. Marcello Rambaldi & Emmanuel Bacry & Jean-Franc{c}ois Muzy, 2018. "Disentangling and quantifying market participant volatility contributions," Papers 1807.07036, arXiv.org.
    11. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    12. Hyoeun Lee & Kiseop Lee, 2020. "Optimal execution with liquidity risk in a diffusive order book market," Papers 2004.10951, arXiv.org.
    13. Nico Achtsis & Dirk Nuyens, 2013. "A Monte Carlo method for optimal portfolio executions," Papers 1312.5919, arXiv.org.
    14. Christopher Lorenz & Alexander Schied, 2013. "Drift dependence of optimal trade execution strategies under transient price impact," Finance and Stochastics, Springer, vol. 17(4), pages 743-770, October.
    15. Thibault Jaisson & Mathieu Rosenbaum, 2015. "Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes," Papers 1504.03100, arXiv.org.
    16. Masamitsu Ohnishi & Makoto Shimoshimizu, 2022. "Optimal Pair–Trade Execution with Generalized Cross–Impact," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(2), pages 253-289, June.
    17. Kim, Gunhee & Choe, Geon Ho, 2019. "Limit properties of continuous self-exciting processes," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    18. Aurélien Alfonsi & José Infante Acevedo, 2014. "Optimal execution and price manipulations in time-varying limit order books," Post-Print hal-00687193, HAL.
    19. 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.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00971369. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.