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

Reserve Bank of New Zealand Discussion Paper No. 2012/02

Midwest Finance Association 2013 Annual Meeting Paper

51 Pages Posted: 1 Sep 2012

Multiple version iconThere are 4 versions of this paper

Date Written: March 31, 2012

Abstract

With nominal interest rates near the zero lower bound (ZLB) in many major economies, it is theoretically untenable to apply Gaussian affine 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.

Keywords: zero lower bound, shadow short rate, term structure model

JEL Classification: E43, G12, G13

Suggested Citation

Krippner, Leo, Modifying Gaussian Term Structure Models When Interest Rates are Near the Zero Lower Bound (March 31, 2012). Reserve Bank of New Zealand Discussion Paper No. 2012/02, Midwest Finance Association 2013 Annual Meeting Paper, Available at SSRN: https://ssrn.com/abstract=2139510 or http://dx.doi.org/10.2139/ssrn.2139510

Leo Krippner (Contact Author)

Reserve Bank of New Zealand ( email )

2 The Terrace
PO Box 2498
Wellington, 6140
New Zealand

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