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Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification test for Affine Term Structure Models

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  • Torben G. Andersen
  • Luca Benzoni

Abstract

We investigate whether bonds span the volatility risk in the U.S. Treasury market, as predicted by most 'affine' term structure models. To this end, we construct powerful and model-free empirical measures of the quadratic yield variation for a cross-section of fixed-maturity zero-coupon bonds ("realized yield volatility") through the use of high-frequency data. We find that the yield curve fails to span yield volatility, as the systematic volatility factors are largely unrelated to the cross-section of yields. We conclude that a broad class of affine diffusive, Gaussian-quadratic and affine jump-diffusive models is incapable of accommodating the observed yield volatility dynamics. An important implication is that the bond markets per se are incomplete and yield volatility risk cannot be hedged by taking positions solely in the Treasury bond market. We also advocate using the empirical realized yield volatility measures more broadly as a basis for specification testing and (parametric) model selection within the term structure literature.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 12962.

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Date of creation: Mar 2007
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Publication status: published as Torben G. Andersen & Luca Benzoni, 2010. "Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 65(2), pages 603-653, 04.
Handle: RePEc:nbr:nberwo:12962

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Cited by:
  1. Corsi, Fulvio & Fusari, Nicola & La Vecchia, Davide, 2013. "Realizing smiles: Options pricing with realized volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 107(2), pages 284-304.
  2. Peter Christoffersen & Christian Dorion & Kris Jacobs & Lotfi Karoui, 2012. "Nonlinear Kalman Filtering in Affine Term Structure Models," CREATES Research Papers 2012-49, School of Economics and Management, University of Aarhus.
  3. Xavier Gabaix, 2007. "Linearity-Generating Processes: A Modelling Tool Yielding Closed Forms for Asset Prices," NBER Working Papers 13430, National Bureau of Economic Research, Inc.
  4. Don H Kim, 2007. "Spanned stochastic volatility in bond markets: a reexamination of the relative pricing between bonds and bond options," BIS Working Papers 239, Bank for International Settlements.
  5. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series, Federal Reserve Bank of Chicago WP-08-14, Federal Reserve Bank of Chicago.
  6. Refet S. G�rkaynak & Jonathan H. Wright, 2012. "Macroeconomics and the Term Structure," Journal of Economic Literature, American Economic Association, vol. 50(2), pages 331-67, June.
  7. Christensen, Jens H.E. & Lopez, Jose A. & Rudebusch, Glenn D., 2014. "Can spanned term structure factors drive stochastic yield volatility?," Working Paper Series, Federal Reserve Bank of San Francisco 2014-3, Federal Reserve Bank of San Francisco.
  8. Juneja, Januj, 2014. "Term structure estimation in the presence of autocorrelation," The North American Journal of Economics and Finance, Elsevier, Elsevier, vol. 28(C), pages 119-129.
  9. Christensen, Jens H.E. & Rudebusch, Glenn D., 2013. "Modeling yields at the zero lower bound: are shadow rates the solution?," Working Paper Series, Federal Reserve Bank of San Francisco 2013-39, Federal Reserve Bank of San Francisco.
  10. Jens H.E. Christensen, 2013. "A regime-switching model of the yield curve at the zero bound," Working Paper Series, Federal Reserve Bank of San Francisco 2013-34, Federal Reserve Bank of San Francisco.

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