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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 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.

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Paper provided by Reserve Bank of New Zealand in its series Reserve Bank of New Zealand Discussion Paper Series with number DP2012/02.

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Length: 49 p.
Date of creation: Mar 2012
Date of revision:
Handle: RePEc:nzb:nzbdps:2012/02
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  1. Leo Krippner, 2009. "A theoretical foundation for the Nelson and Siegel class of yield curve models," Reserve Bank of New Zealand Discussion Paper Series DP2009/10, Reserve Bank of New Zealand.
  2. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
  3. Langetieg, Terence C, 1980. " A Multivariate Model of the Term Structure," Journal of Finance, American Finance Association, vol. 35(1), pages 71-97, March.
  4. Jens H. E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2008. "An Arbitrage-Free Generalized Nelson-Siegel Term Structure Model," PIER Working Paper Archive 08-030, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  5. Leo Krippner, 2012. "A theoretical foundation for the Nelson and Siegel class of yield curve models," CAMA Working Papers 2012-11, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  6. Wu, Tao, 2006. "Macro Factors and the Affine Term Structure of Interest Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(7), pages 1847-1875, October.
  7. Black, Fischer, 1995. " Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-76, December.
  8. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
  9. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  10. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
  11. Jose Vicente & Benjamin M. Tabak, 2007. "Forecasting Bonds Yields in the Brazilian Fixed Income Market," Working Papers Series 141, Central Bank of Brazil, Research Department.
  12. Scott Joslin & Kenneth J. Singleton & Haoxiang Zhu, 2011. "A New Perspective on Gaussian Dynamic Term Structure Models," Review of Financial Studies, Society for Financial Studies, vol. 24(3), pages 926-970.
  13. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
  14. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  15. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-89, October.
  16. Berardi, Andrea, 2009. "Term Structure, Inflation, and Real Activity," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(04), pages 987-1011, August.
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