  We consider a model for interest rates, where the short rate is given by a
time-homogenous, one-dimensional affine process in the sense of Duffie,
Filipovic and Schachermayer. We show that in such a model yield curves can only
be normal, inverse or humped (i.e. endowed with a single local maximum). Each
case can be characterized by simple conditions on the present short rate. We
give conditions under which the short rate process will converge to a limit
distribution and describe the limit distribution in terms of its cumulant
generating function. We apply our results to the Vasicek model, the CIR model,
a CIR model with added jumps and a model of Ornstein-Uhlenbeck type.
