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Modelling jumps with CARMA(p,q)-Hawkes: An application to corporate bond markets

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  • Mercuri, Lorenzo
  • Perchiazzo, Andrea
  • Rroji, Edit

Abstract

In this paper, we employ the CARMA(p,q)-Hawkes model to investigate the intraday jumps observed in the corporate bond prices. We introduce a bivariate extension of the model, which deals with the cross-effect of upward and downward price movements. An empirical analysis is conducted on green and brown bonds with analogous characteristics. The findings indicate that higher-order univariate/bivariate CARMA(p,q)-Hawkes models produce a superior fit in jump activity with respect to Hawkes models with exponential kernels.

Suggested Citation

  • Mercuri, Lorenzo & Perchiazzo, Andrea & Rroji, Edit, 2025. "Modelling jumps with CARMA(p,q)-Hawkes: An application to corporate bond markets," Finance Research Letters, Elsevier, vol. 73(C).
    • Handle: RePEc:eee:finlet:v:73:y:2025:i:c:s1544612324015927
    DOI: 10.1016/j.frl.2024.106563
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    References listed on IDEAS

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    1. Brockwell, Peter J. & Davis, Richard A. & Yang, Yu, 2011. "Estimation for Non-Negative Lévy-Driven CARMA Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(2), pages 250-259.
    2. Li, Xiaoqian & Ma, Xiaoqi, 2023. "Jumps and gold futures volatility prediction," Finance Research Letters, Elsevier, vol. 58(PC).
    3. 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.
    4. Peter J. Brockwell & Richard A. Davis & Yu Yang, 2011. "Estimation for Non-Negative Lévy-Driven CARMA Processes," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(2), pages 250-259, April.
    5. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
    6. Lee, Kyungsub, 2023. "Recurrent neural network based parameter estimation of Hawkes model on high-frequency financial data," Finance Research Letters, Elsevier, vol. 55(PA).
    7. Asmerilda Hitaj & Lorenzo Mercuri & Edit Rroji, 2019. "Lévy CARMA models for shocks in mortality," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 205-227, June.
    8. Kyungsub Lee, 2023. "Recurrent neural network based parameter estimation of Hawkes model on high-frequency financial data," Papers 2304.11883, arXiv.org.
    9. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    10. Zeng, Qing & Lu, Xinjie & Li, Tao & Wu, Lan, 2022. "Jumps and stock market variance during the COVID-19 pandemic: Evidence from international stock markets," Finance Research Letters, Elsevier, vol. 48(C).
    11. Benth, Fred Espen & Klüppelberg, Claudia & Müller, Gernot & Vos, Linda, 2014. "Futures pricing in electricity markets based on stable CARMA spot models," Energy Economics, Elsevier, vol. 44(C), pages 392-406.
    12. Mercuri, Lorenzo & Perchiazzo, Andrea & Rroji, Edit, 2024. "A Hawkes model with CARMA(p,q) intensity," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 1-26.
    13. repec:taf:jnlbes:v:30:y:2012:i:2:p:242-255 is not listed on IDEAS
    14. 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.
    15. Kaj Nyström & Changyong Zhang, 2022. "Hawkes-based models for high frequency financial data," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 73(10), pages 2168-2185, October.
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    Keywords

    Hawkes; CARMA; Jumps; Green bonds;
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