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A model for interest rates with clustering effects

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  • Donatien Hainaut

    (ESC [Rennes] - ESC Rennes School of Business)

Abstract

We propose a model for short-term rates driven by a self-exciting jump process to reproduce the clustering of shocks on the Euro overnight index average (EONIA). The key element of the model is the feedback eect between the absolute value of jumps and the intensity of their arrival process. In this setting, we obtain a closed-form solution for the characteristic function for interest rates and their integral. We introduce a class of equivalent measures under which the features of the process are preserved. We infer the prices of bonds and their dynamics under a risk-neutral measure. The question of derivatives pricing is developed under a forward measure, and a numerical algorithm is proposed to evaluate caplets and oorlets. The model is tted to EONIA rates from 2004 to 2014 using a peaks-over-threshold procedure. From observation of swap curves over the same period, we lter the evolution of risk premiums for Brownian and jump components. Finally, we analyze the sensitivity of implied caplet volatility to parameters dening the level of self-excitation.

Suggested Citation

  • Donatien Hainaut, 2016. "A model for interest rates with clustering effects," Post-Print hal-01393994, HAL.
    • Handle: RePEc:hal:journl:hal-01393994
    DOI: 10.1080/14697688.2015.1135251
    Note: View the original document on HAL open archive server: https://rennes-sb.hal.science/hal-01393994
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Xinglin Yang & Ji Chen, 2021. "VIX term structure: The role of jump propagation risks," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(6), pages 785-810, June.
    2. Hainaut, Donatien, 2016. "A bivariate Hawkes process for interest rate modeling," Economic Modelling, Elsevier, vol. 57(C), pages 180-196.
    3. Olivier Le Courtois & François Quittard-Pinon & Xiaoshan Su, 2020. "Pricing and hedging defaultable participating contracts with regime switching and jump risk," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 303-339, June.
    4. Ketelbuters, John-John & Hainaut, Donatien, 2022. "CDS pricing with fractional Hawkes processes," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1139-1150.
    5. Hainaut, Donatien & Goutte, Stephane, 2018. "A switching microstructure model for stock prices," LIDAM Discussion Papers ISBA 2018014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Donatien Hainaut & Franck Moraux, 2019. "A switching self-exciting jump diffusion process for stock prices," Annals of Finance, Springer, vol. 15(2), pages 267-306, June.
    7. Hainaut, Donatien, 2019. "Credit risk modelling with fractional self-excited processes," LIDAM Discussion Papers ISBA 2019027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Hainaut, Donatien, 2017. "Contagion modeling between the financial and insurance markets with time changed processes," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 63-77.
    9. Hainaut, Donatien, 2020. "Credit risk modelling with fractional self-excited processes," LIDAM Discussion Papers ISBA 2020002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Njike Leunga, Charles Guy & Hainaut, Donatien, 2019. "Interbank Credit Risk Modelling with Self-Exciting Jump Processes," LIDAM Discussion Papers ISBA 2019017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Hainaut, Donatien, 2021. "Lévy interest rate models with a long memory," LIDAM Discussion Papers ISBA 2021020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Zeitsch, Peter J., 2019. "A jump model for credit default swaps with hierarchical clustering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 737-775.
    13. Chen, Li & Ma, Yong & Xiao, Weilin, 2022. "Pricing defaultable bonds under Hawkes jump-diffusion processes," Finance Research Letters, Elsevier, vol. 47(PB).
    14. Jean-Loup Dupret & Donatien Hainaut, 2025. "A fractional Hawkes process for illiquidity modeling," Mathematics and Financial Economics, Springer, volume 19, number 6, September.

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