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


  • Andersen is at the Kellogg School of Management, Northwestern University, NBER, and the Center for Research in Econometric Analysis of Time Series (CREATES). Benzoni is at the Federal Reserve Bank of Chicago. We are grateful to Jefferson Duarte, Darrell Duffie, Michael Fleming, Bob Goldstein, Mike Johannes, Chris Jones, Rick Nelson, Jun Pan, Rob Stambaugh (the Editor), Sam Thompson, an anonymous referee, and seminar participants at Carnegie Mellon University, the Chicago Fed, HEC Montréal, Indiana University, the University of Chicago, the Federal Reserve Board of Governors, the St. Louis Fed, the University of Illinois at Chicago, the University of Wisconsin at Madison, the University of Iowa, as well as the Third T.N. Thiele Symposium on Stochastic Volatility, the 2005 International Conference on “Capital Markets, Corporate Finance, Money and Banking” at the Cass Business School, London, the 2006 Econometric Society Winter Meeting, the 2006 CIREQ-CIRANO-MITACS Financial Econometrics Conference, the 2006 Bank of Canada Conference on Fixed Income Markets, the Multivariate Modeling and Risk Management Conference, Sandbjerg, Denmark, the March 2006 NBER Asset Pricing Meeting, the 2007 AFA conference, and the 2007 Chicago Conference on Volatility and High Frequency Data for helpful comments and suggestions. Further, we thank Mitch Haviv of GovPX for providing useful information on their data. Andrea Ajello, Olena Chyruk, and Huiyan Qiu provided outstanding research assistance. Of course, all errors remain our sole responsibility. Andersen's work is supported by a grant from the National Science Foundation to NBER and from CREATES, funded by the Danish National Research Foundation. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve System.


We propose using model-free yield quadratic variation measures computed from intraday data as a tool for specification testing and selection of dynamic term structure models. We find that the yield curve fails to span realized yield volatility in the U.S. Treasury market, as the systematic volatility factors are largely unrelated to the cross-section of yields. We conclude that a broad class of affine diffusive, quadratic Gaussian, and affine jump-diffusive models cannot accommodate the observed yield volatility dynamics. Hence, the Treasury market per se is incomplete, as yield volatility risk cannot be hedged solely through Treasury securities.