Term-structure modelling at the zero lower bound: Implications for estimating the forward term premium

•We estimate affine and quadratic term-structure models for the US Treasury market.•Forward term premium under the zero lower bound is biased under affine model.•The bias increases with the horizon of the expected future interest rates.

Although the affine Gaussian term-structure model has been a workhorse model in term-structure modelling, it remains doubtful whether it is an appropriate model in a low interest rate environment. This paper uses an alternative quadratic Gaussian-term structure model which is well known to be as tractable as the affine model and yet is suitable for interest rates close to zero. Compared with the quadratic model under the zero lower bound, we illustrate how the forward term premium can be biased upward under the affine model both theoretically and empirically.