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Lévy Interest Rate Models with a Long Memory

Author

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  • Donatien Hainaut

    (UCLouvain, LIDAM, Louvain-La-Neueve, 1348 Ottignies-Louvain-la-Neuve, Belgium
    Current address: 20 Voie du Roman Pays, Louvain-La-Neuve, 1348 Ottignies-Louvain-la-Neuve, 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

  • Donatien Hainaut, 2021. "Lévy Interest Rate Models with a Long Memory," Risks, MDPI, vol. 10(1), pages 1-28, December.
    • Handle: RePEc:gam:jrisks:v:10:y:2021:i:1:p:2-:d:709975
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    References listed on IDEAS

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    1. 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.
    2. Boero, G. & Torricelli, C., 1996. "A comparative evaluation of alternative models of the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 93(1), pages 205-223, August.
    3. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
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