Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification Test for Affine Term Structure Models
61 Pages Posted: 15 Mar 2006 Last revised: 25 Jun 2008
Date Written: May 23, 2008
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.
Keywords: Interest Rate Volatility, Hedging, Volatility Risk, Unspanned Stochastic Volatility, Affine Models, Term Structure Models
JEL Classification: E43, G12
Suggested Citation: Suggested Citation