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.
|Date of creation:||Mar 2012|
|Date of revision:|
|Contact details of provider:|| Postal: P.O. Box 2498, Wellington|
Phone: 64 4 471-3767
Fax: 64 4 471-2270
Web page: http://www.rbnz.govt.nz
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Glenn D. Rudebusch, 2010.
"Macro-Finance Models Of Interest Rates And The Economy,"
University of Manchester, vol. 78(s1), pages 25-52, 09.
- Glenn D. Rudebusch, 2010. "Macro-finance models of interest rates and the economy," Working Paper Series 2010-01, Federal Reserve Bank of San Francisco.
- 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.
- Vicente, José & Tabak, Benjamin M., 2008. "Forecasting bond yields in the Brazilian fixed income market," International Journal of Forecasting, Elsevier, vol. 24(3), pages 490-497.
- 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.
- Black, Fischer, 1995. " Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-76, December.
- Jens H.E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2008.
"An Arbitrage-Free Generalized Nelson-Siegel Term Structure Model,"
NBER Working Papers
14463, National Bureau of Economic Research, Inc.
- 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, vol. 12(3), pages C33-C64, November.
- 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.
- Jens H. E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2008. "An arbitrage-free generalized Nelson-Siegel term structure model," Working Paper Series 2008-07, Federal Reserve Bank of San Francisco.
- Langetieg, Terence C, 1980. " A Multivariate Model of the Term Structure," Journal of Finance, American Finance Association, vol. 35(1), pages 71-97, March.
- 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.
- Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
- 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.
- Francis X. Diebold & Canlin Li, 2002.
"Forecasting the Term Structure of Government Bond Yields,"
Center for Financial Institutions Working Papers
02-34, Wharton School Center for Financial Institutions, University of Pennsylvania.
- 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.
- Francis X. Diebold & Canlin Li, 2003. "Forecasting the Term Structure of Government Bond Yields," NBER Working Papers 10048, National Bureau of Economic Research, Inc.
- Diebold, Francis X. & Li, Canlin, 2003. "Forecasting the term structure of government bond yields," CFS Working Paper Series 2004/09, Center for Financial Studies (CFS).
- 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.
- 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.
- 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.
- 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.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:nzb:nzbdps:2012/02. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Reserve Bank of New Zealand Knowledge Centre)
If references are entirely missing, you can add them using this form.