Bond Pricing when the Short-Term Interest Rate Follows a Threshold Process

Abstract

This paper derives analytical solutions for arbitrage-free bond yields when the short-term interest rate follows an autoregressive process with the intercept switching endogenously. This process from the SETAR family is especially suited to capture the near-unit-root behavior typically observed in the evolution of short-term interest rates. The derived yield functions, mapping the one-month rate into n-period yields, exhibit a convex/concave shape to the left and the right of the threshold value, respectively; a pattern which is also found in US bond yield data. The longer the time to maturity, the more distinct the nonlinearity of the yield function becomes.