  This work is denoted to studying the tail behavior of Cox-Ingersoll-Ross
(CIR) processes with regime-switching. One essential difference shown in this
work between CIR process with regime-switching and without regime-switching is
that the stationary distribution for CIR process with regime-switching could be
heavy-tailed. Our results provide a theoretical evidence of the existence of
regime-switching for interest rates model based on its heavy-tailed empirical
evidence. In this work, we first provide sharp criteria to justify the
existence of stationary distribution for the CIR process with regime-switching,
which is applied to study the long term returns of interest rates. Then under
the existence of the stationary distribution, we provide a criterion to justify
whether its stationary distribution is heavy-tailed or not.
