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We consider a model for interest rates, where the short rate is given by atime-homogenous, one-dimensional affine process in the sense of Duffie,Filipovic and Schachermayer. We show that in such a model yield curves can onlybe normal, inverse or humped (i.e. endowed with a single local maximum). Eachcase can be characterized by simple conditions on the present short rate. Wegive conditions under which the short rate process will converge to a limitdistribution and describe the limit distribution in terms of its cumulantgenerating 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.

Yield Curve Shapes and the Asymptotic Short Rate Distribution in Affine One-Factor Models