The asymptotic behavior of the term structure of interest rates

In this dissertation we investigate long-term interest rates, i.e.
interest rates with maturity going to infinity, in the post-crisis
interest rate market. Three different concepts of long-term
interest rates are considered for this purpose: the long-term
yield, the long-term simple rate, and the long-term swap rate. We
analyze the properties as well as the interrelations of these
long-term interest rates. In particular, we study the asymptotic
behavior of the term structure of interest rates in some specific
models. First, we compute the three long-term interest rates in the
HJM framework with different stochastic drivers, namely Brownian
motions, Lévy processes, and affine processes on the state space of
positive semidefinite symmetric matrices. The HJM setting presents
the advantage that the entire yield curve can be modeled directly.
Furthermore, by considering increasingly more general classes of
drivers, we were able to take into account the impact of different
risk factors and their dependence structure on the long end of the
yield curve. Finally, we study the long-term interest rates and
especially the long-term swap rate in the Flesaker-Hughston model
and the linear-rational methodology.