I develop an interest rate model with separate factors driving innovations in bond yields and their covariances. It features a flexible and tractable affine structure for bond covariances. Maximum likelihood estimation of the model with panel data on swaptions and discount bonds implies pricing errors for swaptions that are almost always lower than half of the bid–ask spread. Furthermore, market prices of interest rate caps do not deviate significantly from their no‐arbitrage values implied by the swaptions under the model. These findings support the conjectures of Collin‐Dufresne and Goldstein (2003) , Dai and Singleton (2003) , and Jagnnathan, Kaplin, and Sun (2003) .

We study an important recent series of buyback auctions conducted by the U.S. Treasury in retiring $67.5 billion of its illiquid off‐the‐run debt. The Treasury was successful in buying back large amounts of illiquid debt while suffering only a small market‐impact cost. The Treasury included the most‐illiquid bonds more frequently in the auctions, but tended to buy back the least‐illiquid of these bonds. Although the Treasury had the option to cherry pick from among the bonds offered, we find that the Treasury was actually penalized for being spread too thinly in the buybacks.