  We investigate the joint description of the interest-rate term stuctures of
Italy and an AAA-rated European country by mean of a --here proposed--
correlated CIR-like bivariate model where one of the state variables is
interpreted as a benchmark risk-free rate and the other as a credit spread. The
model is constructed by requiring the strict positivity of interest rates and
the asymptotic decoupling of the joint distribution of the two state variables
on a long time horizon. The second condition is met by imposing the
reversibility of the process with respect to a product measure, the first is
then implemented by using the tools of potential theory. It turns out that
these conditions select a class of non-affine models, out of which we choose
one that is quadratic in the two state variables both in the drift and
diffusion matrix. We perform a numerical analysis of the model by investigating
a cross section of the term structures comparing the results with those
obtained with an uncoupled bivariate CIR model.
