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Can interest rate volatility be extracted from the cross section of bond yields?

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  • Collin-Dufresne, Pierre
  • Goldstein, Robert S.
  • Jones, Christopher S.

Abstract

Most affine models of the term structure with stochastic volatility predict that the variance of the short rate should play a 'dual role' in that it should also equal a linear combination of yields. However, we find that estimation of a standard affine three-factor model results in a variance state variable that, while instrumental in explaining the shape of the yield curve, is essentially unrelated to GARCH estimates of the quadratic variation of the spot rate process or to implied variances from options. We then investigate four-factor affine models. Of the models tested, only the model that exhibits 'unspanned stochastic volatility' (USV) generates both realistic short rate volatility estimates and a good cross-sectional fit. Our findings suggest that short rate volatility cannot be extracted from the cross-section of bond prices. In particular, short rate volatility and convexity are only weakly correlated.

Suggested Citation

  • Collin-Dufresne, Pierre & Goldstein, Robert S. & Jones, Christopher S., 2009. "Can interest rate volatility be extracted from the cross section of bond yields?," Journal of Financial Economics, Elsevier, vol. 94(1), pages 47-66, October.
  • Handle: RePEc:eee:jfinec:v:94:y:2009:i:1:p:47-66
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    1. repec:eee:ejores:v:262:y:2017:i:3:p:1116-1135 is not listed on IDEAS
    2. Anna Cieslak & Pavol Povala, 2016. "Information in the Term Structure of Yield Curve Volatility," Journal of Finance, American Finance Association, vol. 71(3), pages 1393-1436, June.
    3. Shin, Minchul & Zhong, Molin, 2017. "Does realized volatility help bond yield density prediction?," International Journal of Forecasting, Elsevier, vol. 33(2), pages 373-389.
    4. TAKAMIZAWA, Hideyuki, 2017. "A Term Structure Model of Interest Rates with Quadratic Volatility," Working Paper Series G-1-18, Center for Financial Research, Graduate School of Commerce and Management, Hitotsubashi University.
    5. repec:eme:aecozz:s0731-905320150000035003 is not listed on IDEAS
    6. Laurini, Márcio P. & Caldeira, João F., 2016. "A macro-finance term structure model with multivariate stochastic volatility," International Review of Economics & Finance, Elsevier, vol. 44(C), pages 68-90.
    7. repec:hal:journl:peer-00732517 is not listed on IDEAS
    8. Márcio Laurini & João Frois Caldeira, 2012. "Some Comments on a Macro-Finance Model with Stochastic Volatility," IBMEC RJ Economics Discussion Papers 2012-04, Economics Research Group, IBMEC Business School - Rio de Janeiro.
    9. Hideyuki Takamizawa, 2015. "Predicting Interest Rate Volatility Using Information on the Yield Curve," International Review of Finance, International Review of Finance Ltd., vol. 15(3), pages 347-386, September.
    10. 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.
    11. Filipović, Damir & Gourier, Elise & Mancini, Loriano, 2016. "Quadratic variance swap models," Journal of Financial Economics, Elsevier, vol. 119(1), pages 44-68.
    12. Anh Le & Bruno Feunou & Christian Lundblad & Jean-Sébastien Fontaine, 2015. "Tractable Term-Structure Models and the Zero Lower Bound," Staff Working Papers 15-46, Bank of Canada.
    13. Christensen, Jens H.E. & Lopez, Jose A. & Rudebusch, Glenn D., 2014. "Can Spanned Term Structure Factors Drive Stochastic Yield Volatility?," Working Paper Series 2014-3, Federal Reserve Bank of San Francisco.
    14. Peter Feldhütter, 2016. "Can Affine Models Match the Moments in Bond Yields?," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 1-56, June.
    15. 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.
    16. Breach , Tomas & D'Amico, Stefania & Orphanides, Athanasios, 2016. "The Term Structure and Inflation Uncertainty," Working Paper Series WP-2016-22, Federal Reserve Bank of Chicago.
    17. Jerry Tsai, 2013. "Rare Disasters and the Term Structure of Interest Rates," Economics Series Working Papers 665, University of Oxford, Department of Economics.
    18. Almeida, Caio & Graveline, Jeremy J. & Joslin, Scott, 2011. "Do interest rate options contain information about excess returns?," Journal of Econometrics, Elsevier, vol. 164(1), pages 35-44, September.
    19. Lin-Yee Hin & Nikolai Dokuchaev, 2016. "Short Rate Forecasting Based On The Inference From The Cir Model For Multiple Yield Curve Dynamics," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-33, March.
    20. 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.
    21. Takamizawa, Hideyuki, 2015. "Impact of No-arbitrage on Interest Rate Dynamics," Working Paper Series G-1-5, Center for Financial Research, Graduate School of Commerce and Management, Hitotsubashi University.

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