A term structure interest rate model with the Brownian bridge lower bound

Abstract

We present a new quadratic Gaussian short rate model with a stochastic lower bound to capture changes in the yield curve including negative interest rates, associated with changes in monetary policy stances. We model the lower bound by a Brownian bridge pinned at zero at the initial time and at a random termination time, representing the first appearance of negative interest rates and the end date of an unconventional monetary policy, respectively. Within this framework, we derive a semi-analytical pricing formula for zero coupon bonds under the no-arbitrage condition. Our model estimation results using Japanese yield curve data show a good fit to the market data. Furthermore, the expected excess bond returns and the posterior distribution of the unconventional monetary policy duration computed from the model parameter and state variable estimates clarify the market’s perspective on monetary policy developments.