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A tractable framework for zero-lower-bound Gaussian term structure models

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  • Leo Krippner

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.

Suggested Citation

  • Leo Krippner, 2013. "A tractable framework for zero-lower-bound Gaussian term structure models," CAMA Working Papers 2013-49, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  • Handle: RePEc:een:camaaa:2013-49
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    References listed on IDEAS

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    1. 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 33-64, November.
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    7. Krippner, Leo, 2013. "Measuring the stance of monetary policy in zero lower bound environments," Economics Letters, Elsevier, vol. 118(1), pages 135-138.
    8. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    9. Leo Krippner, 2011. "Modifying Gaussian term structure models when interest rates are near the zero lower bound," CAMA Working Papers 2011-36, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    10. Michael D. Bauer & Glenn D. Rudebusch, 2016. "Monetary Policy Expectations at the Zero Lower Bound," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 48(7), pages 1439-1465, October.
    11. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155.
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    15. Diebold, Francis X. & Rudebusch, Glenn D. & Borag[caron]an Aruoba, S., 2006. "The macroeconomy and the yield curve: a dynamic latent factor approach," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 309-338.
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    Cited by:

    1. Gavin, William T. & Keen, Benjamin D. & Richter, Alexander & Throckmorton, Nathaniel, 2013. "The stimulative effect of forward guidance," Working Papers 2013-38, Federal Reserve Bank of St. Louis, revised 30 Apr 2014.
    2. Christensen, Jens H.E. & Lopez, Jose A. & Rudebusch, Glenn D., 2015. "A probability-based stress test of Federal Reserve assets and income," Journal of Monetary Economics, Elsevier, vol. 73(C), pages 26-43.
    3. Leo Krippner, 2014. "Measuring the stance of monetary policy in conventional and unconventional environments," CAMA Working Papers 2014-06, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    4. von Borstel, Julia & Eickmeier, Sandra & Krippner, Leo, 2016. "The interest rate pass-through in the euro area during the sovereign debt crisis," Journal of International Money and Finance, Elsevier, vol. 68(C), pages 386-402.
    5. repec:eme:aecozz:s0731-905320150000035003 is not listed on IDEAS
    6. Yakov Ben-Haim & Maria Demertzis & Jan Willem Van den End, 2017. "Fundamental uncertainty and unconventional monetary policy: an info-gap approach," DNB Working Papers 544, Netherlands Central Bank, Research Department.
    7. repec:eee:finlet:v:21:y:2017:i:c:p:100-106 is not listed on IDEAS
    8. Jens H. E. Christensen & Glenn D. Rudebusch, 2016. "Modeling Yields at the Zero Lower Bound: Are Shadow Rates the Solution?," Advances in Econometrics,in: Dynamic Factor Models, volume 35, pages 75-125 Emerald Publishing Ltd.
    9. Jing Cynthia Wu & Fan Dora Xia, 2016. "Measuring the Macroeconomic Impact of Monetary Policy at the Zero Lower Bound," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 48(2-3), pages 253-291, March.
    10. Marcello Pericoli & Marco Taboga, 2015. "Understanding policy rates at the zero lower bound: insights from a Bayesian shadow rate model," Temi di discussione (Economic working papers) 1023, Bank of Italy, Economic Research and International Relations Area.
    11. Stephen Hansen & Michael McMahon, 2016. "Shocking Language: Understanding the Macroeconomic Effects of Central Bank Communication," NBER Chapters,in: NBER International Seminar on Macroeconomics 2015 National Bureau of Economic Research, Inc.
    12. Adam Kucera & Michal Dvorak & Lubos Komarek & Zlatuse Komarkova, 2017. "Longer-term Yield Decomposition: An Analysis of the Czech Government Yield Curve," Working Papers 2017/12, Czech National Bank, Research Department.
    13. repec:eee:ecofin:v:43:y:2018:i:c:p:87-96 is not listed on IDEAS
    14. Mariarosaria Comunale & Jonas Striaukas, 2017. "Unconventional monetary policy: interest rates and low inflation: A review of literature and methods," CAMA Working Papers 2017-29, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    15. repec:eee:ecolet:v:156:y:2017:i:c:p:118-122 is not listed on IDEAS
    16. Leo Krippner, 2013. "Efficient Jacobian evaluations for estimating zero lower bound term structure models," CAMA Working Papers 2013-77, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    17. Christensen, Jens H. E., 2013. "A Regime-Switching Model of the Yield Curve at the Zero Bound," Working Paper Series 2013-34, Federal Reserve Bank of San Francisco, revised 29 Apr 2015.
    18. repec:bla:ecinqu:v:55:y:2017:i:4:p:1593-1624 is not listed on IDEAS
    19. Dora Xia & Jing Cynthia Wu, 2018. "The negative interest rate policy and the yield curve," BIS Working Papers 703, Bank for International Settlements.
    20. Edda Claus & Iris Claus & Leo Krippner, 2014. "Asset markets and monetary policy shocks at the zero lower bound," Reserve Bank of New Zealand Discussion Paper Series DP2014/03, Reserve Bank of New Zealand.
    21. Marco Jacopo Lombardi & Feng Zhu, 2014. "A shadow policy rate to calibrate US monetary policy at the zero lower bound," BIS Working Papers 452, Bank for International Settlements.

    More about this item

    Keywords

    zero lower bound; term structure of interest rates; Gaussian affine term structure models; shadow short rate; shadow term structure;

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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