RFS Advance Access originally published online on January 14, 2008
Review of Financial Studies 2008 21(2):819-854; doi:10.1093/rfs/hhm082
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Identifying Term Structure Volatility from the LIBOR-Swap Curve
Arrowstreet Capital
Address correspondence to Samuel Thompson, Arrowstreet Capital, L.P., 44 Brattle Street, 5th Floor, Cambridge, MA 02138; telephone: (617) 547-9999; fax: (617) 547-0099; e-mail: sambthompson{at}gmail.com
JEL Classification: C52, G13
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Abstract |
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This paper proposes a new family of specification tests and applies them to affine term structure models of the London Interbank Offered Rate (LIBOR)-swap curve. Contrary to Dai and Singleton (2000), the tests show that when standard estimation techniques are used, affine models do a poor job of forecasting volatility at the short end of the term structure. Improving the volatility forecast does not require different models; rather, it requires a different estimation technique. The paper distinguishes between two econometric procedures for identifying volatility. The "cross-sectional" approach backs out volatility from a cross section of bond yields, and the "time-series" approach imputes volatility from time-series variation in yields. For an affine model, the volatility implied by the time-series procedure passes the specification tests, while the cross-sectionally identified volatility does not. This is surprising, since under correct specification, the "cross-sectional" approach is maximum likelihood. One explanation is that affine models are slightly misspecified; another is that bond yields do not span volatility, as in Collin-Dufresne and Goldstein (2002).
I am indebted to Thomas Rothenberg for his invaluable advice. This paper is based on my dissertation, which he supervised. I thank Donald Andrews, John Campbell, Gary Chamberlain, Kjell Doksum, Chris Foote, Petra Geraats, Angelo Melino, James Powell, Matt Pritsker, Paul Ruud, Neil Shephard, Ken Singleton, Richard Stanton, Jeremy Stein, Jim Stock, Tim Vogelsang, and Tuomo Vuolteenaho for useful comments. I am also grateful for the comments of seminar participants at Cornell University, the Helsinki School of Economics, the Massachusetts Institute of Technology, Northeastern University, Rice University, and Yale University. Advice from Yacine Ait-Sahalia and two anonymous referees improved the exposition of the paper. Many of the calculations were carried out using Mathematica code provided by Yacine Ait-Sahalia and Robert Kimmel, and by Gauss code provided by Yongmiao Hong and Haitao Li.