Exponential-affine bond pricing ($P_{t,T}=e^{\alpha (T-t)X_t+\beta (T-t)}$)

If a discrete-time martingale deflator obeys $Y_t/Y_{t-1}=e^{X_t}$ for an affine process $X$, unit zero-coupon bonds have exponential-affine prices. For one-step coefficients $A,B$, the recursion is $\alpha (0)=\beta (0)=0$, $\alpha (n+1)=A(1+\alpha (n))$, $\beta (n+1)=\beta (n)+B(1+\alpha (n))$.