  We provide a full classification of all attainable term structure shapes in
the two-factor Vasicek model of interest rates. In particular, we show that the
shapes normal, inverse, humped, dipped and hump-dip are always attainable. In
certain parameter regimes up to four additional shapes can be produced. Our
results apply to both forward and yield curves and show that the correlation
and the difference in mean-reversion speeds of the two factor processes play a
key role in determining the scope of attainable shapes. The key mathematical
tool is the theory of total positivity, pioneered by Samuel Karlin and others
in the 1950ies.
