A Term Structure Interest Rate Model with the Exit Time from the Negative Interest Rate Policy

In the government bond markets in Japan and a number of European countries, neg-ative interest rates have been observed in recent years. Incorporating a negative lowerbound for interest rates into a term structure model makes it possible for the model toreplicate yield curves that include negative rates. In this study, we propose a new termstructure model with a stochastic lower bound where the short rate is de ned as the sumof the quadratic form of the Gaussian process and a negative lower bound for interestrates. The lower bound is characterized by a Brownian bridge with the random intervalpinned 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 theno arbitrage condition. We calibrate our proposed model using Japanese yield curve dataand estimate the implied posterior distribution of the time to exit from the NIRP.