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  [ 4 ],  [ 5 ], and  [ 25 ], and the long-term simple rate, considered in  [ 8 ] 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  .
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 .
A
Biagini et al.
R
4
2018
A
Biagini and H\"artel
R
5
2014
A
El Karoui et al.
R
25
1997
A
Brody and Hughston
R
8
2016
A
. A numerical example illustrates how our results can be used to estimate the non-optional component of a CoCo bond