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Multi-kernel property in high-frequency price dynamics under Hawkes model

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  • Kyungsub Lee

Abstract

This study investigates and uses multi-kernel Hawkes models to describe a high-frequency mid-price process. Each kernel represents a different responsive speed of market participants. Using the conditional Hessian, we examine whether the numerical optimizer effectively finds the global maximum of the log-likelihood function under complicated modeling. Empirical studies that use stock prices in the US equity market show the existence of multi-kernels classified as ultra-high-frequency (UHF), very-high-frequency (VHF), and high-frequency (HF). We estimate the conditional expectations of arrival times and the degree of contribution to the high-frequency activities for each kernel.

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  • Kyungsub Lee, 2023. "Multi-kernel property in high-frequency price dynamics under Hawkes model," Papers 2302.11822, arXiv.org.
    • Handle: RePEc:arx:papers:2302.11822
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    References listed on IDEAS

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    1. Hyun Jin Jang & Kiseop Lee & Kyungsub Lee, 2020. "Systemic risk in market microstructure of crude oil and gasoline futures prices: A Hawkes flocking model approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(2), pages 247-275, February.
    2. 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.
    3. 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.
    4. Kyungsub Lee & Byoung Ki Seo, 2022. "Modeling bid and ask price dynamics with an extended Hawkes process and its empirical applications for high-frequency stock market data," Papers 2201.10173, arXiv.org.
    5. 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.
    6. Emmanuel Bacry & Jean-Fran�ois Muzy, 2014. "Hawkes model for price and trades high-frequency dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1147-1166, July.
    7. 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.
    8. Arouri, Mohamed & M’saddek, Oussama & Nguyen, Duc Khuong & Pukthuanthong, Kuntara, 2019. "Cojumps and asset allocation in international equity markets," Journal of Economic Dynamics and Control, Elsevier, vol. 98(C), pages 1-22.
    9. Arouri, Mohamed & M’saddek, Oussama & Nguyen, Duc Khuong & Pukthuanthong, Kuntara, 2019. "Cojumps and asset allocation in international equity markets," Journal of Economic Dynamics and Control, Elsevier, vol. 98(C), pages 1-22.
    10. Hasbrouck, Joel & Saar, Gideon, 2009. "Technology and liquidity provision: The blurring of traditional definitions," Journal of Financial Markets, Elsevier, vol. 12(2), pages 143-172, May.
    11. Choi, So Eun & Jang, Hyun Jin & Lee, Kyungsub & Zheng, Harry, 2021. "Optimal market-Making strategies under synchronised order arrivals with deep neural networks," Journal of Economic Dynamics and Control, Elsevier, vol. 125(C).
    12. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    13. Emmanuel Bacry & Thibault Jaisson & Jean--François Muzy, 2016. "Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1179-1201, August.
    14. Ketelbuters, John-John & Hainaut, Donatien, 2022. "CDS pricing with fractional Hawkes processes," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1139-1150.
    15. Large, Jeremy, 2007. "Measuring the resiliency of an electronic limit order book," Journal of Financial Markets, Elsevier, vol. 10(1), pages 1-25, February.
    16. Ketelbuters, John John & Hainaut, Donatien, 2022. "CDS Pricing with Fractional Hawkes Processes," LIDAM Reprints ISBA 2022002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. 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.
    18. 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.
    19. P. A. W Lewis & G. S. Shedler, 1979. "Simulation of nonhomogeneous poisson processes by thinning," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(3), pages 403-413, September.
    20. Alan G. Hawkes, 2018. "Hawkes processes and their applications to finance: a review," Quantitative Finance, Taylor & Francis Journals, vol. 18(2), pages 193-198, February.
    21. 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.
    22. 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.
    23. 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).
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