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Behavior Of Long-Term Yields In A Lévy Term Structure

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  • FRANCESCA BIAGINI

    (Department of Mathematics, LMU University, Theresienstrasse 39, D-80333 Munich, Germany)

  • MAXIMILIAN HÄRTEL

    (Department of Mathematics, LMU University, Theresienstrasse 39, D-80333 Munich, Germany)

Abstract

We study the behavior of the long-term yield in a HJM setting for forward rates driven by Lévy processes. The long-term rates are investigated by examining continuously compounded spot rate yields with maturity going to infinity. In this paper, we generalize the model of Karoui et al. (1997) by using Lévy processes instead of Brownian motions as driving processes of the forward rate dynamics, and analyze the behavior of the long-term yield under certain conditions which encompass the asymptotic behavior of the interest rate model's volatility function as well as the variation of the paths of the Lévy process. One of the main results is that the long-term volatility has to vanish except in the case of a Lévy process with only negative jumps and paths of finite variation serving as random driver. Furthermore, we study the required asymptotic behavior of the volatility function so that the long-term drift exists.

Suggested Citation

  • Francesca Biagini & Maximilian Härtel, 2014. "Behavior Of Long-Term Yields In A Lévy Term Structure," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(03), pages 1-24.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:03:n:s0219024914500162
    DOI: 10.1142/S0219024914500162
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    References listed on IDEAS

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    1. Jan de Kort, 2018. "A note on the long rate in factor models of the term structure," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 656-667, April.
    2. Sebastián A. Rey, 2016. "Theory of long-term interest rates," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-18, September.

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