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Modifying Gaussian term structure models when interest rates are near the zero lower bound (this is a revised version of CAMA working paper 36/2011)

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  • Leo Krippner

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Abstract

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.

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File URL: http://cama.crawford.anu.edu.au/pdf/working-papers/2012/052012.pdf
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Bibliographic Info

Paper provided by Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University in its series CAMA Working Papers with number 2012-05.

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Length: 48 pages
Date of creation: Feb 2012
Date of revision:
Handle: RePEc:een:camaaa:2012-05

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  1. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
  2. Jens H. E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2009. "An arbitrage-free generalized Nelson--Siegel term structure model," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 12(3), pages C33-C64, November.
  3. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, Elsevier, vol. 130(2), pages 337-364, February.
  4. 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.
  5. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 363-84, March.
  6. Wu, Tao, 2006. "Macro Factors and the Affine Term Structure of Interest Rates," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 38(7), pages 1847-1875, October.
  7. Berardi, Andrea, 2009. "Term Structure, Inflation, and Real Activity," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 44(04), pages 987-1011, August.
  8. Langetieg, Terence C, 1980. " A Multivariate Model of the Term Structure," Journal of Finance, American Finance Association, American Finance Association, vol. 35(1), pages 71-97, March.
  9. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 177-188, November.
  10. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 60(4), pages 473-89, October.
  11. Black, Fischer, 1995. " Interest Rates as Options," Journal of Finance, American Finance Association, American Finance Association, vol. 50(5), pages 1371-76, December.
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