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Lévy interest rate models with a long memory

Author

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  • Hainaut, Donatien

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

This article proposes an interest rate model ruled by mean reverting Lévy processes with a sub-exponential memory of their sample path. This feature is achieved by considering an Ornstein- Uhlenbeck process in which the exponential decaying kernel is replaced by a Mittag-Leffler function. Based on a representation in term of an infinite dimensional Markov processes, we present the main characteristics of bonds and short-term rates in this setting. Their dynamics under risk neutral and forward measures are studied. Finally, bond options are valued with a discretization scheme and a discrete Fourier's transform.

Suggested Citation

  • 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).
    • Handle: RePEc:aiz:louvad:2021020
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    References listed on IDEAS

    as
    1. Njike Leunga, Charles Guy & Hainaut, Donatien, 2020. "Interbank credit risk modeling with self-exciting jump processes," LIDAM Reprints ISBA 2020027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    8. Li, Haitao & Ye, Xiaoxia & Yu, Fan, 2020. "Unifying Gaussian dynamic term structure models from a Heath–Jarrow–Morton perspective," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1153-1167.
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    13. Donatien Hainaut, 2016. "A model for interest rates with clustering effects," Post-Print hal-01393994, HAL.
    14. Moreno, Manuel & Platania, Federico, 2015. "A cyclical square-root model for the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 241(1), pages 109-121.
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