A Tractable Framework for Zero-Lower-Bound Gaussian Term Structure Models

67 Pages Posted: 17 Aug 2013 Last revised: 20 Jan 2014

Date Written: August 1, 2013

Abstract

When nominal interest rates are near their zero lower bound (ZLB), as in many developed economies at the time of writing, it is theoretically untenable to apply the popular class of Gaussian affine term structure models (GATSMs) given their inherent material probabilities of negative interest rates. Hence, I propose a tractable modification for GATSMs that enforces the ZLB, and which approximates the fully arbitrage-free but much less tractable framework proposed in Black (1995). I apply my framework to United States yield curve data, with robust estimation via the iterated extended Kalman filter, and first show that the two-factor results are very similar to those from a comparable Black model. I then estimate two- and three-factor models with longer-maturity data sets to illustrate that my ZLB framework can readily be applied in circumstances would computationally burdensome or infeasible within the Black framework.

Keywords: zero lower bound, term structure of interest rates, Gaussian affine term structure models, shadow short rate, shadow term structure

JEL Classification: E43, G12, G13

Suggested Citation

Krippner, Leo, A Tractable Framework for Zero-Lower-Bound Gaussian Term Structure Models (August 1, 2013). CAMA Working Paper No. 49/2013. Available at SSRN: https://ssrn.com/abstract=2310990 or http://dx.doi.org/10.2139/ssrn.2310990

Leo Krippner (Contact Author)

Reserve Bank of New Zealand ( email )

2 The Terrace
PO Box 2498
Wellington, 6140
New Zealand

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