Zero coupon bonds and affine term structures: reconsidering the one-factor model

We consider the pricing of a zero coupon bond with maturity T in the presence of an affine term structure, linear drift and an affine diffusion coefficient. By using standard techniques of differential calculus and the theory of linear diffusions, we derive the value of the bond and demonstrate that the derivation of its value is closely related to the derivation of the decreasing minimal excessive function for a reflected regular diffusion.