  We study the term structure equation for single-factor models that predict
nonnegative short rates. In particular, we show that the price of a bond or a
bond option is the unique classical solution to a parabolic differential
equation with a certain boundary behavior for vanishing values of the short
rate. If the boundary is attainable then this boundary behavior serves as a
boundary condition and guarantees uniqueness of solutions. On the other hand,
if the boundary is nonattainable then the boundary behavior is not needed to
guarantee uniqueness but it is nevertheless very useful, for instance, from a
numerical perspective.
