  The paper is devoted to the study of the short rate equation of the form $$ d
R(t)=F(R(t)) dt+\sum_{i=1}^{d}G_i(R(t-)) dZ_i(t), \quad R(0)=x\geq 0,\quad t>0,
$$ with deterministic functions $F,G_1,...,G_d$ and a multivariate L\'evy
process $Z=(Z_1,...,Z_d)$. The equation is supposed to have a nonnegative
solution which generates an affine term structure model. Two classes of noise
are considered. In the first one the coordinates of Z are independent processes
with regularly varying Laplace exponents. In the second class Z is a spherical
processes, which means that its L\'evy measure has a similar structure as that
of a stable process, but with radial part of a general form. For both classes a
precise form of the short rate generator is characterized. Under mild
assumptions it is shown that any equation of the considered type has the same
solution as the equation driven by a L\'evy process with independent stable
coordinates.
  The paper generalizes the classical results on the Cox-Ingersoll-Ross (CIR)
model as well as on its extended version where $Z$ is a one-dimensional L\'evy
process.
