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General Analysis Of Long-Term Interest Rates

Author

Listed:
  • FRANCESCA BIAGINI

    (Department of Mathematics, LMU University, Theresienstrasse 39, D-80333 Munich, Germany2Department of Mathematics, University of Oslo, Box 1053, Blindern, 0316 Oslo, Norway)

  • ALESSANDRO GNOATTO

    (Department of Economics, University of Verona, Via Cantarane 24, 37129 Verona, Italy)

  • MAXIMILIAN HÄRTEL

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

Abstract

We introduce here the idea of a long-term swap rate, characterized as the fair rate of an overnight indexed swap (OIS) with infinitely many exchanges. Furthermore, we analyze the relationship between the long-term swap rate, the long-term yield, (F. Biagini, A. Gnoatto & M. Härtel (2018) Affine HJM Framework on Sd+ and long-term yield, Applied Mathematics and Optimization 77 (3), 405–441, F. Biagini & M. Härtel (2014) Behavior of long-term yields in a lévy term structure, International Journal of Theoretical and Applied Finance 17 (3), 1–24, N. El Karoui, A. Frachot & H. Geman (1997) A note on the behavior of long zero coupon rates in a no arbitrage framework. Working Paper. Available at Researchgate: https://www.researchgate.net/publication/5066730), and the long-term simple rate (D. C. Brody & L. P. Hughston (2016) Social discounting and the long rate of interest, Mathematical Finance 28 (1), 306–334) as long-term discounting rate. Finally, we investigate the existence of these long-term rates in two-term structure methodologies, the Flesaker–Hughston model and the linear-rational model. A numerical example illustrates how our results can be used to estimate the nonoptional component of a CoCo bond.

Suggested Citation

  • Francesca Biagini & Alessandro Gnoatto & Maximilian Härtel, 2020. "General Analysis Of Long-Term Interest Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-29, January.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:01:n:s0219024920500028
    DOI: 10.1142/S0219024920500028
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    References listed on IDEAS

    as
    1. Damiano Brigo & João Garcia & Nicola Pede, 2015. "Coco Bonds Pricing With Credit And Equity Calibrated First-Passage Firm Value Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-31.
    2. Constantinos Kardaras & Eckhard Platen, 2009. "On the Dybvig-Ingersoll-Ross Theorem," Papers 0901.2080, arXiv.org, revised Mar 2010.
    3. Shiller, Robert J, 1979. "The Volatility of Long-Term Interest Rates and Expectations Models of the Term Structure," Journal of Political Economy, University of Chicago Press, vol. 87(6), pages 1190-1219, December.
    4. Filipović, Damir & Trolle, Anders B., 2013. "The term structure of interbank risk," Journal of Financial Economics, Elsevier, vol. 109(3), pages 707-733.
    5. Marek Rutkowski, 1997. "A note on the Flesaker-Hughston model of the term structure of interest rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(3), pages 151-163.
    6. Schulze, Klaas, 2008. "Asymptotic Maturity Behavior of the Term Structure," Bonn Econ Discussion Papers 11/2008, University of Bonn, Bonn Graduate School of Economics (BGSE).
    7. Dybvig, Philip H & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1996. "Long Forward and Zero-Coupon Rates Can Never Fall," The Journal of Business, University of Chicago Press, vol. 69(1), pages 1-25, January.
    8. Damir Filipović & Martin Larsson & Anders B. Trolle, 2017. "Linear-Rational Term Structure Models," Journal of Finance, American Finance Association, vol. 72(2), pages 655-704, April.
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