  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.
