Modeling volatility in dynamic term structure models

We propose no-arbitrage term structure models with volatility factors that follow GARCH processes. The models' tractability is similar to canonical affine term structure models, but they fit yield volatility much better, especially for long-maturity yields. This improvement does not come at the expense of a deterioration in yield fit. Because of the improved volatility fit, the model performs substantially better in pricing Treasury futures options. We conclude that the specification of the volatility factors is critical. Modeling volatility as a function of (lagged) squared innovations to factors improves on models where volatility is a linear function of the factors.