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).