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Can spanned term structure factors drive stochastic yield volatility?

  • Christensen, Jens H.E.

    ()

    (Federal Reserve Bank of San Francisco)

  • Lopez, Jose A.

    ()

    (Federal Reserve Bank of San Francisco)

  • Rudebusch, Glenn D.

    ()

    (Federal Reserve Bank of San Francisco)

The ability of the usual factors from empirical arbitrage-free representations of the term structure—that is, spanned factors—to account for interest rate volatility dynamics has been much debated. We examine this issue with a comprehensive set of new arbitrage-free term structure specifications that allow for spanned stochastic volatility to be linked to one or more of the yield curve factors. Using U.S. Treasury yields, we find that much realized stochastic volatility cannot be associated with spanned term structure factors. However, a simulation study reveals that the usual realized volatility metric is misleading when yields contain plausible measurement noise. We argue that other metrics should be used to validate stochastic volatility models.

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Paper provided by Federal Reserve Bank of San Francisco in its series Working Paper Series with number 2014-3.

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Length: 30 pages
Date of creation: Jan 2014
Date of revision:
Handle: RePEc:fip:fedfwp:2014-03
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  1. Ruslan Bikbov & Mikhail Chernov, 2009. "Unspanned Stochastic Volatility in Affine Models: Evidence from Eurodollar Futures and Options," Management Science, INFORMS, vol. 55(8), pages 1292-1305, August.
  2. Hautsch, Nikolaus & Ou, Yangguoyi, 2012. "Analyzing interest rate risk: Stochastic volatility in the term structure of government bond yields," Journal of Banking & Finance, Elsevier, vol. 36(11), pages 2988-3007.
  3. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
  4. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2008. "Inflation expectations and risk premiums in an arbitrage-free model of nominal and real bond yields," Working Paper Series 2008-34, Federal Reserve Bank of San Francisco.
  5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  6. Koopman, Siem Jan & Mallee, Max I. P. & Van der Wel, Michel, 2010. "Analyzing the Term Structure of Interest Rates Using the Dynamic Nelson–Siegel Model With Time-Varying Parameters," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 329-343.
  7. Jens H. E. Christensen & Glenn D. Rudebusch, 2012. "The response of interest rates to U.S. and U.K. quantitative easing," Working Paper Series 2012-06, Federal Reserve Bank of San Francisco.
  8. Pierre Collin-Dufresne & Robert S. Goldstein, 2002. "Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility," Journal of Finance, American Finance Association, vol. 57(4), pages 1685-1730, 08.
  9. Duffee, Gregory R, 1999. "Estimating the Price of Default Risk," Review of Financial Studies, Society for Financial Studies, vol. 12(1), pages 197-226.
  10. Torben G. Andersen & Luca Benzoni, 2006. "Do bonds span volatility risk in the U.S. Treasury market? a specification test for affine term structure models," Working Paper Series WP-06-15, Federal Reserve Bank of Chicago.
  11. Jagannathan, Ravi & Kaplin, Andrew & Sun, Steve, 2003. "An evaluation of multi-factor CIR models using LIBOR, swap rates, and cap and swaption prices," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 113-146.
  12. 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.
  13. Jacobs, Kris & Karoui, Lotfi, 2009. "Conditional volatility in affine term-structure models: Evidence from Treasury and swap markets," Journal of Financial Economics, Elsevier, vol. 91(3), pages 288-318, March.
  14. Michael D. Bauer & Glenn D. Rudebusch & Jing Cynthia Wu, 2012. "Correcting Estimation Bias in Dynamic Term Structure Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 454-467, April.
  15. 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.
  16. 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.
  17. Joost Driessen, 2005. "Is Default Event Risk Priced in Corporate Bonds?," Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 165-195.
  18. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2014. "Do Central Bank Liquidity Facilities Affect Interbank Lending Rates?," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 136-151, January.
  19. 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, 02.
  20. Ruslan Bikbov & Mikhail Chernov, 2011. "Yield Curve and Volatility: Lessons from Eurodollar Futures and Options," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(1), pages 66-105, Winter.
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