# The Long-Term Swap Rate and a General Analysis of Long-Term Interest Rates

Source: [The Long-Term Swap Rate and a General Analysis of Long-Term Interest Rates](<https://www.sota2.com/research/paper/68fa7ca81e209131cea8f05b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T06:05:59.268Z

Authors: Francesca Biagini, Alessandro Gnoatto, Maximilian H\\"artel

Published: 2015-07-01T12:38:51.000Z

## Abstract

We introduce here for the first time the long-term swap rate, characterised as the fair rate of an overnight indexed swap with infinitely many exchanges. Furthermore we analyse the relationship between the long-term swap rate, the long-term yield, see Biagini et al. \[2018\], Biagini and H\\"artel \[2014\], and El Karoui et al. \[1997\], and the long-term simple rate, considered in Brody and Hughston \[2016\] as long-term discounting rate. We finally 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 non-optional component of a CoCo bond.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1507.00208>)

[PDF](<https://arxiv.org/pdf/1507.00208.pdf>)