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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

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

We investigate whether bonds span the volatility risk in the U.S. Treasury market, as predicted by most `a±ne' term structure models. To this end, we construct powerful and model-free empirical measures of the quadratic yield variation for a cross-section of ¯xed-maturity zero-coupon bonds (`realized yield volatility') through the use of high-frequency data. We ¯nd 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 a±ne di®usive, Gaussian-quadratic and a±ne jump-di®usive 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 speci¯cation testing and (parametric) model selection within the term structure literature.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2007-25.

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Length: 59
Date of creation: 17 Sep 2007
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Handle: RePEc:aah:create:2007-25

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Cited by:
  1. 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.
  2. 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.
  3. Corsi, Fulvio & Fusari, Nicola & La Vecchia, Davide, 2013. "Realizing smiles: Options pricing with realized volatility," Journal of Financial Economics, Elsevier, vol. 107(2), pages 284-304.
  4. Gürkaynak, Refet S. & Wright, Jonathan, 2010. "Macroeconomics and the Term Structure," CEPR Discussion Papers 8018, C.E.P.R. Discussion Papers.
  5. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
  6. Christensen, Jens H.E. & Rudebusch, Glenn D., 2013. "Modeling yields at the zero lower bound: are shadow rates the solution?," Working Paper Series 2013-39, Federal Reserve Bank of San Francisco.
  7. Jens H.E. Christensen, 2013. "A regime-switching model of the yield curve at the zero bound," Working Paper Series 2013-34, Federal Reserve Bank of San Francisco.
  8. Peter Christoffersen & Christian Dorion & Kris Jacobs & Lotfi Karoui, 2014. "Nonlinear Kalman Filtering in Affine Term Structure Models," Cahiers de recherche 1404, CIRPEE.
  9. 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.
  10. 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.

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