Modifying Gaussian Term Structure Models When Interest Rates are Near the Zero Lower Bound

With nominal interest rates near the zero lower bound (ZLB) in many major economies, it has become untenable to apply Gaussian affine term structure models (GATSMs) while ignoring their inherent theoretical deficiency of non-zero probabilities of negative interest rates. In this article I propose correcting that deficiency by adjusting the entire GATSM term structure with an explicit function of maturity that represents the optionality associated with the present and future availability of physical currency. The resulting ZLB-GATSM framework remains tractable, producing a simple closed-form analytic expression for forward rates and requiring only elementary univariate numerical integration (over time to maturity) to obtain interest rates and bond prices. I demonstrate the salient features of the ZLB-GATSM framework using a two-factor model. An illustrative application to U.S. term structure data indicates that movements in the model state variables have been consistent with unconventional monetary policy easings undertaken after the U.S. policy rate reached the ZLB in late 2008