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GENERAL ANALYSIS OF LONG-TERM INTEREST RATES

FRANCESCA BIAGINI

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

Department of Mathematics, University of Oslo, Box 1053, Blindern, 0316 Oslo, Norway

E-mail Address: [email protected]

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ALESSANDRO GNOATTO

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

E-mail Address: [email protected]

Corresponding author.

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, and

MAXIMILIAN HÄRTEL

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

E-mail Address: [email protected]

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https://doi.org/10.1142/S0219024920500028Cited by:1 (Source: Crossref)

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 $S_{d}^{+}$ and long-term yield, Applied Mathematics and Optimization77 (3), 405–441, F. Biagini & M. Härtel (2014) Behavior of long-term yields in a lévy term structure, International Journal of Theoretical and Applied Finance17 (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 Finance28 (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.

Keywords:

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