IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2307.09077.html
   My bibliography  Save this paper

Estimation of an Order Book Dependent Hawkes Process for Large Datasets

Author

Listed:
  • Luca Mucciante
  • Alessio Sancetta

Abstract

A point process for event arrivals in high frequency trading is presented. The intensity is the product of a Hawkes process and high dimensional functions of covariates derived from the order book. Conditions for stationarity of the process are stated. An algorithm is presented to estimate the model even in the presence of billions of data points, possibly mapping covariates into a high dimensional space. The large sample size can be common for high frequency data applications using multiple liquid instruments. Convergence of the algorithm is shown, consistency results under weak conditions is established, and a test statistic to assess out of sample performance of different model specifications is suggested. The methodology is applied to the study of four stocks that trade on the New York Stock Exchange (NYSE). The out of sample testing procedure suggests that capturing the nonlinearity of the order book information adds value to the self exciting nature of high frequency trading events.

Suggested Citation

  • Luca Mucciante & Alessio Sancetta, 2023. "Estimation of an Order Book Dependent Hawkes Process for Large Datasets," Papers 2307.09077, arXiv.org.
    • Handle: RePEc:arx:papers:2307.09077
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2307.09077
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Grossman, Sanford J & Stiglitz, Joseph E, 1980. "On the Impossibility of Informationally Efficient Markets," American Economic Review, American Economic Association, vol. 70(3), pages 393-408, June.
    2. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Endogenous Liquidity Crises," Post-Print hal-02567495, HAL.
    3. V. Filimonov & D. Sornette, 2015. "Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1293-1314, August.
    4. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2019. "Endogenous Liquidity Crises," Papers 1912.00359, arXiv.org, revised Feb 2020.
    5. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    6. Matthias Kirchner, 2017. "An estimation procedure for the Hawkes process," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 571-595, April.
    7. José Da Fonseca & Riadh Zaatour, 2014. "Hawkes Process: Fast Calibration, Application to Trade Clustering, and Diffusive Limit," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(6), pages 548-579, June.
    8. Rama Cont & Arseniy Kukanov & Sasha Stoikov, 2014. "The Price Impact of Order Book Events," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 47-88.
    9. Hall, Anthony D. & Hautsch, Nikolaus, 2007. "Modelling the buy and sell intensity in a limit order book market," Journal of Financial Markets, Elsevier, vol. 10(3), pages 249-286, August.
    10. Sancetta, Alessio, 2018. "Estimation For The Prediction Of Point Processes With Many Covariates," Econometric Theory, Cambridge University Press, vol. 34(3), pages 598-627, June.
    11. Xuefeng Gao & Lingjiong Zhu, 2018. "Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 161-206, October.
    12. Othmane Mounjid & Mathieu Rosenbaum & Pamela Saliba, 2019. "From asymptotic properties of general point processes to the ranking of financial agents," Papers 1906.05420, arXiv.org.
    13. Alec N. Kercheval & Yuan Zhang, 2015. "Modelling high-frequency limit order book dynamics with support vector machines," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1315-1329, August.
    14. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2022. "State-dependent Hawkes processes and their application to limit order book modelling," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 563-583, March.
    15. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Endogenous Liquidity Crises," Working Papers hal-02567495, HAL.
    Full references (including those not matched with items on IDEAS)

    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. Konark Jain & Nick Firoozye & Jonathan Kochems & Philip Treleaven, 2024. "Limit Order Book Simulations: A Review," Papers 2402.17359, arXiv.org, revised Mar 2024.
    2. Michele Vodret & Iacopo Mastromatteo & Bence Tóth & Michael Benzaquen, 2023. "Microfounding GARCH models and beyond: a Kyle-inspired model with adaptive agents," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(3), pages 599-625, July.
    3. Matthew F Dixon, 2017. "Sequence Classification of the Limit Order Book using Recurrent Neural Networks," Papers 1707.05642, arXiv.org.
    4. Jean-Philippe Bouchaud, 2021. "The Inelastic Market Hypothesis: A Microstructural Interpretation," Papers 2108.00242, arXiv.org, revised Jan 2022.
    5. Jean-Philippe Bouchaud, 2021. "Radical Complexity," Papers 2103.09692, arXiv.org.
    6. Maxime Morariu-Patrichi & Mikko Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," CREATES Research Papers 2018-26, Department of Economics and Business Economics, Aarhus University.
    7. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," Papers 1809.08060, arXiv.org, revised Sep 2021.
    8. Yue Zhao & Difang Wan, 2018. "Institutional high frequency trading and price discovery: Evidence from an emerging commodity futures market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(2), pages 243-270, February.
    9. Huang, Lorick & Khabou, Mahmoud, 2023. "Nonlinear Poisson autoregression and nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 201-241.
    10. Hautsch, Nikolaus & Jeleskovic, Vahidin, 2008. "Modelling high-frequency volatility and liquidity using multiplicative error models," SFB 649 Discussion Papers 2008-047, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    11. Matthew F Dixon, 2017. "A High Frequency Trade Execution Model for Supervised Learning," Papers 1710.03870, arXiv.org, revised Dec 2017.
    12. repec:hum:wpaper:sfb649dp2008-047 is not listed on IDEAS
    13. Kyungsub Lee, 2024. "Discrete Hawkes process with flexible residual distribution and filtered historical simulation," Papers 2401.13890, arXiv.org.
    14. Alessio Sancetta, 2017. "Estimation for the Prediction of Point Processes with Many Covariates," Papers 1702.05315, arXiv.org.
    15. Thierry Foucault & Ohad Kadan & Eugene Kandel, 2013. "Liquidity Cycles and Make/Take Fees in Electronic Markets," Journal of Finance, American Finance Association, vol. 68(1), pages 299-341, February.
    16. Ping-Chen Tsai & Chi-Ming Tsai, 2021. "Estimating the proportion of informed and speculative traders in financial markets: evidence from exchange rate," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(3), pages 443-470, July.
    17. Ilia Zaznov & Julian Kunkel & Alfonso Dufour & Atta Badii, 2022. "Predicting Stock Price Changes Based on the Limit Order Book: A Survey," Mathematics, MDPI, vol. 10(8), pages 1-33, April.
    18. Arzandeh, Mehdi & Frank, Julieta, 2017. "The Information Content of the Limit Order Book," 7th Annual Canadian Agri-Food Policy Conference, January 11-13, 2017, Ottawa, ON 253251, Canadian Agricultural Economics Society.
    19. Weiyi Liu & Song‐Ping Zhu, 2019. "Pricing variance swaps under the Hawkes jump‐diffusion process," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(6), pages 635-655, June.
    20. Ponta, Linda & Trinh, Mailan & Raberto, Marco & Scalas, Enrico & Cincotti, Silvano, 2019. "Modeling non-stationarities in high-frequency financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 173-196.
    21. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.

    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:arx:papers:2307.09077. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.