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

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.