Conditional Volatility in Affine Term Structure Models : Evidence from Treasury and Swap Markets

Several papers have questioned the ability of multifactor affine models to extract interest rate volatility from the cross-section of yields. These studies find that model-implied conditional volatility is very poorly or even negatively correlated with model-free volatility. We study the ability of three-factor models to extract conditional volatility using interest rate swap yields for 1991-2005 and a sample of Treasury yields for 1970-2003. For the extended Treasury sample, the correlation between model-implied and EGARCH volatility is between 60% and 75%. For swaps,the correlation is rather low or negative. Results for swaps are also more model-dependent and less robust. For Treasuries, a model-free measure of the level factor is highly correlated with EGARCH volatility as well as model-implied volatilities. For swaps, the level factor is not as highly correlated with conditional volatility. We find that these differences in model performance are primarily due to the timing of the swap sample, and not to institutional differences between swap and Treasury markets. Our results are confirmed using metrics other than correlation. They are also robust to the choice of estimation method, interpolation method and volatility measure, and hold for yield ifferences as well as yield levels. We conclude that the ability of multifactor affine models to extract conditional volatility depends on the sample period, but that overall these models perform better than has been argued in the literature