Affine diffusion bond pricing ($P=A(\tau )e^{-B(\tau )r}$)

When ${\mu }_Q=a(b-r)$ and $\eta (r{)}^2={\eta }_0^2+{\eta }_1^{2}r$, substituting $P=A(\tau )e^{-B(\tau )r}$ gives $B^{\prime }=1-aB-{\eta }_1^2{B}^2/2$ and $(\log A{)}^{\prime }=-abB+{\eta }_0^2{B}^2/2$, with $B(0)=0$, $A(0)=1$. The Vasicek model uses ${\eta }_1=0$, and the CIR model uses ${\eta }_0=0$.