In the government bond markets in Japan and a number of European countries, negative interest rates have been observed in recent years. Incorporating a negative lower bound for interest rates into a term structure model makes it possible for the model to replicate yield curves that include negative rates. In this study, we propose a new term structure model with a stochastic lower bound where the short rate is defined as the sum of the quadratic form of the Gaussian process and a negative lower bound for interest rates. The lower bound is characterized by a Brownian bridge with the random interval pinned at zero at the starting time and the end time of a negative interest rate policy (NIRP). Under this setting, we derive a zero coupon bond price formula by imposing the no arbitrage condition. We calibrate our proposed model using Japanese yield curve data and estimate the implied posterior distribution of the time to exit from the NIRP.
A Term Structure Interest Rate Model with the Exit Time from the Negative Interest Rate Policy
DPB19.pp1-15 Kikuchi
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