Using a stochastic discount factor approach, we derive the exact solution for arbitrage-free bond yields for the case that the short-term interest rate follows a threshold process with the intercept switching endogenously. The yield functions, mapping the one-month rate into n-period yields, respectively. This is in contrast to linear short-rate process which imply an affine yield function. The intervals for which convexity or concavity prevails increase with time to maturity.