If one posits the usual two-factor model as either:
df(t, T) = (...)dt + exp(-mrs1*(T-t))*sigma1*dW1 + exp(-mrs2*(T-t))*sigma2*dW2
dr(t) = (theta + u - lambda1*r(t))*dt + sigma1*dW1
u is another correlated OU process
where we assume <dW1, dW2> = rho.dt
then both representations are of course equivalent, but the parameters are not really intuitive, or orthogonal.
For instance, rho is not the only parameter that controls the correlation between short rates and long rates, since the difference in MRS matter too.
Does anyone know of a better more "orthogonal" (i.e. non-overlapping) where one parameter would clearly control the correlation between short rates and long rates ?