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Modifying Gaussian term structure models when interest rates are near the zero lower bound

Leo Krippner

With nominal interest rates near the zero lower bound (ZLB) in many major economies, it is theoretically untenable to apply Gaussian a¢ ne term structure models (GATSMs) while ignoring their inherent material probabilities of negative interest rates. 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 estimation with U.S. term structure data indicates that the ZLB-GATSM "shadow short rate" provides a useful gauge of the stance of monetary policy; in particular becoming negative when the U.S. policy rate reached the ZLB in late 2008, and moving more negative with subsequent unconventional monetary policy easings.