IDEAS home Printed from https://ideas.repec.org/p/een/camaaa/2013-49.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://cama.crawford.anu.edu.au/files/publication/cama_crawford_anu_edu_au/2013-08/49_2013_krippner_1.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    2. Chen, Ren-Raw & Scott, Louis O, 1992. "Pricing Interest Rate Options in a Two-Factor Cox-Ingersoll-Ross Model of the Term Structure," The Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 613-636.
    3. Scott Joslin & Kenneth J. Singleton & Haoxiang Zhu, 2011. "A New Perspective on Gaussian Dynamic Term Structure Models," The Review of Financial Studies, Society for Financial Studies, vol. 24(3), pages 926-970.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. Krippner, Leo, 2013. "Measuring the stance of monetary policy in zero lower bound environments," Economics Letters, Elsevier, vol. 118(1), pages 135-138.
    6. Yoichi Ueno & Naohiko Baba & Yuji Sakurai, 2006. "The Use of the Black Model of Interest Rates as Options for Monitoring the JGB Market Expectations," Bank of Japan Working Paper Series 06-E-15, Bank of Japan.
    7. Cheridito, Patrick & Filipovic, Damir & Kimmel, Robert L., 2007. "Market price of risk specifications for affine models: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 83(1), pages 123-170, January.
    8. Hibiki Ichiue & Yoichi Ueno, 2007. "Equilibrium Interest Rate and the Yield Curve in a Low Interest Rate Environment," Bank of Japan Working Paper Series 07-E-18, Bank of Japan.
    9. 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.
    10. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    11. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    12. Kim, Don H. & Singleton, Kenneth J., 2012. "Term structure models and the zero bound: An empirical investigation of Japanese yields," Journal of Econometrics, Elsevier, vol. 170(1), pages 32-49.
    13. 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.
    14. 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..
    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.
    16. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    17. Black, Fischer, 1995. "Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-1376, December.
    18. Hibiki Ichiue & Yoichi Ueno, 2006. "Monetary Policy and the Yield Curve at Zero Interest: The Macro-Finance Model of Interest Rates as Options," Bank of Japan Working Paper Series 06-E-16, Bank of Japan.
    19. 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, April.
    20. Hibiki Ichiue & Yoichi Ueno, 2013. "Estimating Term Premia at the Zero Bound: An Analysis of Japanese, US, and UK Yields," Bank of Japan Working Paper Series 13-E-8, Bank of Japan.
    21. Dai, Qiang & Singleton, Kenneth J., 2002. "Expectation puzzles, time-varying risk premia, and affine models of the term structure," Journal of Financial Economics, Elsevier, vol. 63(3), pages 415-441, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Monfort, Alain & Pegoraro, Fulvio & Renne, Jean-Paul & Roussellet, Guillaume, 2017. "Staying at zero with affine processes: An application to term structure modelling," Journal of Econometrics, Elsevier, vol. 201(2), pages 348-366.
    4. Andrea Carriero & Sarah Mouabbi & Elisabetta Vangelista, 2018. "UK term structure decompositions at the zero lower bound," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(5), pages 643-661, August.
    5. Yoichi Ueno, 2017. "Term Structure Models with Negative Interest Rates," IMES Discussion Paper Series 17-E-01, Institute for Monetary and Economic Studies, Bank of Japan.
    6. 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.
    7. Istrefi, Klodiana & Mouabbi, Sarah, 2018. "Subjective interest rate uncertainty and the macroeconomy: A cross-country analysis," Journal of International Money and Finance, Elsevier, vol. 88(C), pages 296-313.
    8. Krippner, Leo, 2013. "Measuring the stance of monetary policy in zero lower bound environments," Economics Letters, Elsevier, vol. 118(1), pages 135-138.
    9. Leo Krippner, 2012. "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)," CAMA Working Papers 2012-05, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    10. Martin M. Andreasen & Andrew Meldrum, 2014. "Dynamic term structure models: The best way to enforce the zero lower bound," CREATES Research Papers 2014-47, Department of Economics and Business Economics, Aarhus University.
    11. Matsumura, Marco & Moreira, Ajax & Vicente, José, 2011. "Forecasting the yield curve with linear factor models," International Review of Financial Analysis, Elsevier, vol. 20(5), pages 237-243.
    12. 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.
    13. Andreasen, Martin M & Meldrum, Andrew, 2015. "Dynamic term structure models: the best way to enforce the zero lower bound in the United States," Bank of England working papers 550, Bank of England.
    14. Caldeira, João F. & Laurini, Márcio P. & Portugal, Marcelo S., 2010. "Bayesian Inference Applied to Dynamic Nelson-Siegel Model with Stochastic Volatility," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 30(1), October.
    15. Christensen, Bent Jesper & van der Wel, Michel, 2019. "An asset pricing approach to testing general term structure models," Journal of Financial Economics, Elsevier, vol. 134(1), pages 165-191.
    16. Ichiue, Hibiki & Ueno, Yoichi, 2015. "Monetary policy and the yield curve at zero interest," Journal of the Japanese and International Economies, Elsevier, vol. 38(C), pages 1-12.
    17. Bruno Feunou & Jean-Sébastien Fontaine & Anh Le & Christian Lundblad, 2022. "Tractable Term Structure Models," Management Science, INFORMS, vol. 68(11), pages 8411-8429, November.
    18. Tsz-Kin Chung & Cho-Hoi Hui & Ka-Fai Li, 2015. "Term-Structure Modelling at the Zero Lower Bound: Implications for Estimating the Term Premium," Working Papers 212015, Hong Kong Institute for Monetary Research.
    19. Jens H. E. Christensen & Glenn D. Rudebusch, 2015. "Estimating Shadow-Rate Term Structure Models with Near-Zero Yields," Journal of Financial Econometrics, Oxford University Press, vol. 13(2), pages 226-259.
    20. Michal Dvorák & Zlatuše Komárková & Adam Kucera, 2019. "The Czech Government Yield Curve Decomposition at the Lower Bound," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 69(1), pages 2-36, February.

    More about this item

    Keywords

    zero lower bound; term structure of interest rates; Gaussian affine term structure models; shadow short rate; shadow term structure;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:een:camaaa:2013-49. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Cama Admin (email available below). General contact details of provider: https://edirc.repec.org/data/asanuau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.