IDEAS home Printed from https://ideas.repec.org/a/eee/empfin/v62y2021icp202-219.html
   My bibliography  Save this article

What does a term structure model imply about very long-term interest rates?

Author

Listed:
  • Balter, Anne G.
  • Pelsser, Antoon
  • Schotman, Peter C.

Abstract

We address two empirical issues related to the long end of the yield curve based on euro swap rates. First, for maturities longer than 20 years we find evidence for an ‘excess’ downward slope that cannot be explained by convexity. Second, volatility at the very long end of the yield curve is larger than predicted by no-arbitrage models. We construct a model-based arbitrage-free extrapolation of the yield-curve and compare it to the regulatory discount curve. Because of near-zero mean reversion, there is no convergence towards an ‘ultimate forward rate’ and convexity effects cause the arbitrage-free extrapolations to have slightly downward sloping curves. The low level of mean-reversion also implies that the volatility of long-term rates does not decline relative to the 20-year volatility. Therefore, we conclude that the mean-reversion and resulting smoothing adopted by the regulatory curve is much too strong.

Suggested Citation

  • Balter, Anne G. & Pelsser, Antoon & Schotman, Peter C., 2021. "What does a term structure model imply about very long-term interest rates?," Journal of Empirical Finance, Elsevier, vol. 62(C), pages 202-219.
    • Handle: RePEc:eee:empfin:v:62:y:2021:i:c:p:202-219
    DOI: 10.1016/j.jempfin.2021.03.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0927539821000256
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jempfin.2021.03.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    2. Christensen, Jens H.E. & Diebold, Francis X. & Rudebusch, Glenn D., 2011. "The affine arbitrage-free class of Nelson-Siegel term structure models," Journal of Econometrics, Elsevier, vol. 164(1), pages 4-20, September.
    3. 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.
    4. 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.
    5. de Jong, Frank, 2000. "Time Series and Cross-Section Information in Affine Term-Structure Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 300-314, July.
    6. Robin Greenwood & Annette Vissing-Jorgensen, 2018. "The Impact of Pensions and Insurance on Global Yield Curves," Harvard Business School Working Papers 18-109, Harvard Business School, revised Dec 2018.
    7. 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.
    8. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    9. 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..
    10. Scott Joslin & Marcel Priebsch & Kenneth J. Singleton, 2014. "Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks," Journal of Finance, American Finance Association, vol. 69(3), pages 1197-1233, June.
    11. Hamilton, James D. & Wu, Jing Cynthia, 2012. "Identification and estimation of Gaussian affine term structure models," Journal of Econometrics, Elsevier, vol. 168(2), pages 315-331.
    12. Bams, Dennis & Schotman, Peter C., 2003. "Direct estimation of the risk neutral factor dynamics of Gaussian term structure models," Journal of Econometrics, Elsevier, vol. 117(1), pages 179-206, November.
    13. Riccardo Rebonato & Vladislav Putyatin, 2018. "The value of convexity: a theoretical and empirical investigation," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 11-30, January.
    14. Sven Klingler & Suresh Sundaresan, 2019. "An Explanation of Negative Swap Spreads: Demand for Duration from Underfunded Pension Plans," Journal of Finance, American Finance Association, vol. 74(2), pages 675-710, April.
    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 473-489, October.
    16. Dietrich Domanski & Hyun Song Shin & Vladyslav Sushko, 2017. "The Hunt for Duration: Not Waving but Drowning?," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 65(1), pages 113-153, April.
    17. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    18. de Kort, J. & Vellekoop, M.H., 2016. "Term structure extrapolation and asymptotic forward rates," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 107-119.
    19. 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.
    20. Driessen, Joost & Nijman, Theodore E. & Simon, Zorka, 2022. "A simple approach to estimate long-term interest rates," SAFE Working Paper Series 238, Leibniz Institute for Financial Research SAFE, revised 2022.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Berardi, Andrea & Plazzi, Alberto, 2022. "Dissecting the yield curve: The international evidence," Journal of Banking & Finance, Elsevier, vol. 134(C).
    2. Thomas A. McWalter & Erik Schlögl & Jacques van Appel, 2023. "Analysing Quantiles in Models of Forward Term Rates," Risks, MDPI, vol. 11(2), pages 1-18, January.
    3. Berardi, Andrea, 2023. "Term premia and short rate expectations in the euro area," Journal of Empirical Finance, Elsevier, vol. 74(C).

    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. Januj Amar Juneja, 2022. "A Computational Analysis of the Tradeoff in the Estimation of Different State Space Specifications of Continuous Time Affine Term Structure Models," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 173-220, June.
    2. 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.
    3. 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.
    4. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2021. "No‐arbitrage priors, drifting volatilities, and the term structure of interest rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 495-516, August.
    5. Adrian, Tobias & Crump, Richard K. & Moench, Emanuel, 2013. "Pricing the term structure with linear regressions," Journal of Financial Economics, Elsevier, vol. 110(1), pages 110-138.
    6. Hitesh Doshi & Kris Jacobs & Rui Liu, 2021. "Information in the Term Structure: A Forecasting Perspective," Management Science, INFORMS, vol. 67(8), pages 5255-5277, August.
    7. Yung, Julieta, 2021. "Can interest rate factors explain exchange rate fluctuations?," Journal of Empirical Finance, Elsevier, vol. 61(C), pages 34-56.
    8. Juneja, Januj, 2017. "Invariance, observational equivalence, and identification: Some implications for the empirical performance of affine term structure models," The Quarterly Review of Economics and Finance, Elsevier, vol. 64(C), pages 292-305.
    9. Bruno Feunou & Jean-Sébastien Fontaine & Anh Le & Christian Lundblad, 2022. "Tractable Term Structure Models," Management Science, INFORMS, vol. 68(11), pages 8411-8429, November.
    10. Carriero, Andrea & Kapetanios, George & Marcellino, Massimiliano, 2012. "Forecasting government bond yields with large Bayesian vector autoregressions," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 2026-2047.
    11. Greg Duffee, 2011. "Forecasting with the term structure: The role of no-arbitrage restrictions," Economics Working Paper Archive 576, The Johns Hopkins University,Department of Economics.
    12. Coroneo, Laura & Nyholm, Ken & Vidova-Koleva, Rositsa, 2011. "How arbitrage-free is the Nelson-Siegel model?," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 393-407, June.
    13. Caldeira, João F. & Moura, Guilherme V. & Santos, André A.P., 2016. "Bond portfolio optimization using dynamic factor models," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 128-158.
    14. Han, Yang & Jiao, Anqi & Ma, Jun, 2021. "The predictive power of Nelson–Siegel factor loadings for the real economy," Journal of Empirical Finance, Elsevier, vol. 64(C), pages 95-127.
    15. repec:erh:journl:v:6:y:2014:i:2:p:78-100 is not listed on IDEAS
    16. Juneja, Januj, 2014. "Term structure estimation in the presence of autocorrelation," The North American Journal of Economics and Finance, Elsevier, vol. 28(C), pages 119-129.
    17. Giuseppe Arbia & Michele Di Marcantonio, 2015. "Forecasting Interest Rates Using Geostatistical Techniques," Econometrics, MDPI, vol. 3(4), pages 1-28, November.
    18. Doshi, Hitesh & Jacobs, Kris & Liu, Rui, 2018. "Macroeconomic determinants of the term structure: Long-run and short-run dynamics," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 99-122.
    19. Márcio Poletti Laurini & Armênio Westin Neto, 2014. "Arbitrage in the Term Structure of Interest Rates: a Bayesian Approach," International Econometric Review (IER), Econometric Research Association, vol. 6(2), pages 77-99, September.
    20. Kaya, Huseyin, 2013. "Forecasting the yield curve and the role of macroeconomic information in Turkey," Economic Modelling, Elsevier, vol. 33(C), pages 1-7.
    21. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2010. "Inflation Expectations and Risk Premiums in an Arbitrage‐Free Model of Nominal and Real Bond Yields," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(s1), pages 143-178, September.

    More about this item

    Keywords

    Term structure models; Parameter uncertainty; Extrapolation; Insurance supervision;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

    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:eee:empfin:v:62:y:2021:i:c:p:202-219. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jempfin .

    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.