IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1706.07459.html
   My bibliography  Save this paper

General Compound Hawkes Processes in Limit Order Books

Author

Listed:
  • Anatoliy Swishchuk

Abstract

In this paper, we study various new Hawkes processes, namely, so-called general compound and regime-switching general compound Hawkes processes to model the price processes in the limit order books. We prove Law of Large Numbers (LLN) and Functional Central Limit Theorems (FCLT) for these processes. The latter two FCLTs are applied to limit order books where we use these asymptotic methods to study the link between price volatility and order flow in our two models by studying the diffusion limits of these price processes. The volatilities of price changes are expressed in terms of parameters describing the arrival rates and price changes.

Suggested Citation

  • Anatoliy Swishchuk, 2017. "General Compound Hawkes Processes in Limit Order Books," Papers 1706.07459, arXiv.org, revised Jun 2017.
    • Handle: RePEc:arx:papers:1706.07459
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1706.07459
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Engle, Robert F. & Lange, Joe, 2001. "Predicting VNET: A model of the dynamics of market depth," Journal of Financial Markets, Elsevier, vol. 4(2), pages 113-142, April.
    2. Vladimir Filimonov & Didier Sornette, 2012. "Quantifying reflexivity in financial markets: towards a prediction of flash crashes," Papers 1201.3572, arXiv.org, revised Apr 2012.
    3. Ban Zheng & François Roueff & Frédéric Abergel, 2014. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Post-Print hal-00777941, HAL.
    4. Ban Zheng & Franc{c}ois Roueff & Fr'ed'eric Abergel, 2013. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Papers 1301.5007, arXiv.org, revised Feb 2014.
    5. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    6. 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.
    7. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    8. Patrick J. Laub & Thomas Taimre & Philip K. Pollett, 2015. "Hawkes Processes," Papers 1507.02822, arXiv.org.
    9. Luc, BAUWENS & Nikolaus, HAUTSCH, 2006. "Modelling Financial High Frequency Data Using Point Processes," Discussion Papers (ECON - Département des Sciences Economiques) 2006039, Université catholique de Louvain, Département des Sciences Economiques.
    10. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    11. Anatoliy Swishchuk & Bruno Remillard & Robert Elliott & Jonathan Chavez-Casillas, 2017. "Compound Hawkes Processes in Limit Order Books," Papers 1712.03106, arXiv.org.
    12. Robert F. Engle & Asger Lunde, 2003. "Trades and Quotes: A Bivariate Point Process," Journal of Financial Econometrics, Oxford University Press, vol. 1(2), pages 159-188.
    13. Jonathan A. Ch'avez-Casillas & Robert J. Elliott & Bruno R'emillard & Anatoliy V. Swishchuk, 2017. "A level-1 Limit Order book with time dependent arrival rates," Papers 1704.06572, arXiv.org.
    14. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    15. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
    16. Large, Jeremy, 2007. "Measuring the resiliency of an electronic limit order book," Journal of Financial Markets, Elsevier, vol. 10(1), pages 1-25, February.
    17. Chavez-Demoulin, V. & McGill, J.A., 2012. "High-frequency financial data modeling using Hawkes processes," Journal of Banking & Finance, Elsevier, vol. 36(12), pages 3415-3426.
    18. Anatoliy Swishchuk, 2017. "Risk Model Based on General Compound Hawkes Process," Papers 1706.09038, arXiv.org.
    19. Filimonov, Vladimir & Bicchetti, David & Maystre, Nicolas & Sornette, Didier, 2014. "Quantification of the high level of endogeneity and of structural regime shifts in commodity markets," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 174-192.
    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. Swishchuk, Anatoliy & Zagst, Rudi & Zeller, Gabriela, 2021. "Hawkes processes in insurance: Risk model, application to empirical data and optimal investment," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 107-124.
    2. 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.
    3. Ana Roldan Contreras & Anatoliy Swishchuk, 2022. "Optimal Liquidation, Acquisition and Market Making Problems in HFT under Hawkes Models for LOB," Risks, MDPI, vol. 10(8), pages 1-32, August.
    4. Myles Sjogren & Timothy DeLise, 2021. "General Compound Hawkes Processes for Mid-Price Prediction," Papers 2110.07075, arXiv.org.
    5. Anatoliy Swishchuk & Aiden Huffman, 2018. "General Compound Hawkes Processes in Limit Order Books," Papers 1812.02298, 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. Anatoliy Swishchuk, 2017. "Risk Model Based on General Compound Hawkes Process," Papers 1706.09038, arXiv.org.

    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. Anatoliy Swishchuk & Aiden Huffman, 2018. "General Compound Hawkes Processes in Limit Order Books," Papers 1812.02298, arXiv.org.
    2. Anatoliy Swishchuk, 2021. "Modelling of Limit Order Books by General Compound Hawkes Processes with Implementations," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 399-428, March.
    3. Anatoliy Swishchuk & Bruno Remillard & Robert Elliott & Jonathan Chavez-Casillas, 2017. "Compound Hawkes Processes in Limit Order Books," Papers 1712.03106, arXiv.org.
    4. Anatoliy Swishchuk & Aiden Huffman, 2020. "General Compound Hawkes Processes in Limit Order Books," Risks, MDPI, vol. 8(1), pages 1-25, March.
    5. Hai-Chuan Xu & Wei-Xing Zhou, 2020. "Modeling aggressive market order placements with Hawkes factor models," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-12, January.
    6. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    7. Kyungsub Lee, 2022. "Application of Hawkes volatility in the observation of filtered high-frequency price process in tick structures," Papers 2207.05939, arXiv.org.
    8. Filimonov, Vladimir & Bicchetti, David & Maystre, Nicolas & Sornette, Didier, 2014. "Quantification of the high level of endogeneity and of structural regime shifts in commodity markets," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 174-192.
    9. Swishchuk, Anatoliy & Zagst, Rudi & Zeller, Gabriela, 2021. "Hawkes processes in insurance: Risk model, application to empirical data and optimal investment," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 107-124.
    10. Qi Guo & Bruno Remillard & Anatoliy Swishchuk, 2020. "Multivariate General Compound Point Processes in Limit Order Books," Papers 2008.00124, arXiv.org.
    11. 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.
    12. 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.
    13. Qi Guo & Bruno Remillard & Anatoliy Swishchuk, 2020. "Multivariate General Compound Point Processes in Limit Order Books," Risks, MDPI, vol. 8(3), pages 1-20, September.
    14. repec:hal:wpaper:hal-00777941 is not listed on IDEAS
    15. Wheatley, Spencer & Filimonov, Vladimir & Sornette, Didier, 2016. "The Hawkes process with renewal immigration & its estimation with an EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 120-135.
    16. 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.
    17. Ban Zheng & Franc{c}ois Roueff & Fr'ed'eric Abergel, 2013. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Papers 1301.5007, arXiv.org, revised Feb 2014.
    18. Steffen Volkenand & Günther Filler & Martin Odening, 2020. "Price Discovery and Market Reflexivity in Agricultural Futures Contracts with Different Maturities," Risks, MDPI, vol. 8(3), pages 1-17, July.
    19. Lucio Maria Calcagnile & Giacomo Bormetti & Michele Treccani & Stefano Marmi & Fabrizio Lillo, 2015. "Collective synchronization and high frequency systemic instabilities in financial markets," Papers 1505.00704, arXiv.org.
    20. Giacomo Bormetti & Lucio Maria Calcagnile & Michele Treccani & Fulvio Corsi & Stefano Marmi & Fabrizio Lillo, 2015. "Modelling systemic price cojumps with Hawkes factor models," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1137-1156, July.
    21. Lee, Kyungsub & Seo, Byoung Ki, 2017. "Modeling microstructure price dynamics with symmetric Hawkes and diffusion model using ultra-high-frequency stock data," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 154-183.

    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:1706.07459. 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.