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A bivariate Hawkes process based model, for interest rates

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  • Donatien Hainaut

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

Abstract

This paper proposes a continuous time model for interest rates, based on a bi-variate self exciting point process. The two components of this process represent the global supply and demand for fixed income instruments. In this framework, closed form expressions are obtained for the first moments of the short term rate and for bonds, under an equivalent affine risk neutral measure. European derivatives are priced under a forward measure and a numerical algorithm is proposed to evaluate caplets and floorlets. The model is fitted to the time series of one year swap rates, from 2004 to 2014. From observation of yield curves over the same period, we filter the evolution of risk premiums of supply and demand processes. Finally, we analyze the sensitivity of implied volatilities of caplets to parameters defining the level of mutual-excitation.

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  • Donatien Hainaut, 2016. "A bivariate Hawkes process based model, for interest rates," Post-Print hal-01458162, HAL.
    • Handle: RePEc:hal:journl:hal-01458162
    DOI: 10.1016/j.econmod.2016.04.016
    Note: View the original document on HAL open archive server: https://rennes-sb.hal.science/hal-01458162
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    Cited by:

    1. Dupret, Jean-Loup & Hainaut, Donatien, 2023. "A fractional Hawkes process for illiquidity modeling," LIDAM Discussion Papers ISBA 2023001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Ketelbuters, John-John & Hainaut, Donatien, 2022. "CDS pricing with fractional Hawkes processes," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1139-1150.
    3. 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).
    4. 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).
    5. 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.
    6. 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).
    7. 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).
    8. 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.

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