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Clustering and Mean Reversion in a Hawkes Microstructure Model

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  • José Da Fonseca
  • Riadh Zaatour

Abstract

This paper provides explicit formulas for the first and second moments and the autocorrelation function of the number of jumps over a given interval for the multivariate Hawkes process. These computations are possible thanks to the affine property of this process. We unify the stock price models of Bacry et al. (2013a, Quantitative Finance, 13, 65–77) and Da Fonseca and Zaatour (2014, Journal of Futures Markets) both of them based on the Hawkes process, the first one having a mean reverting behavior while the second one a clustering behavior, and build a model having these two properties. We compute various statistics as well as the diffusive limit for the stock price that determines the connection between the parameters driving the high‐frequency activity to the daily volatility. Lastly, the impulse function giving the impact on the stock price of a buy/sell trade is explicitly computed. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:813–838, 2015

Suggested Citation

  • José Da Fonseca & Riadh Zaatour, 2015. "Clustering and Mean Reversion in a Hawkes Microstructure Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(9), pages 813-838, September.
    • Handle: RePEc:wly:jfutmk:v:35:y:2015:i:9:p:813-838
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    Cited by:

    1. Kramer, Anke & Kiesel, Rüdiger, 2021. "Exogenous factors for order arrivals on the intraday electricity market," Energy Economics, Elsevier, vol. 97(C).
    2. 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.
    3. Benjamin Favetto, 2019. "The European intraday electricity market : a modeling based on the Hawkes process," Working Papers hal-02089289, HAL.
    4. 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).
    5. Dumitru, Ana-Maria & Holden, Tom, 2017. "A Hawkes model of the transmission of European sovereign default risk," EconStor Conference Papers 168431, ZBW - Leibniz Information Centre for Economics.
    6. Liu, Guo & Jin, Zhuo & Li, Shuanming, 2021. "Optimal investment, consumption, and life insurance strategies under a mutual-exciting contagious market," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 508-524.
    7. Dumitru, Ana-Maria & Holden, Thomas, 2019. "Quantifying the transmission of European sovereign default risk," EconStor Preprints 193632, ZBW - Leibniz Information Centre for Economics.
    8. Markus Vogl, 2022. "Quantitative modelling frontiers: a literature review on the evolution in financial and risk modelling after the financial crisis (2008–2019)," SN Business & Economics, Springer, vol. 2(12), pages 1-69, December.
    9. Lee, Kyungsub & Seo, Byoung Ki, 2017. "Marked Hawkes process modeling of price dynamics and volatility estimation," Journal of Empirical Finance, Elsevier, vol. 40(C), pages 174-200.
    10. 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.
    11. 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.

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