Modeling Volatility in Dynamic Term Structure Models

We propose no-arbitrage term structure models in which the volatility factors followGARCH processes. The models’ tractability is similar to that of canonical affine termstructure models, but they capture the conditional variances of yields much more accurately.We estimate a model with one volatility factor using Treasury yield data for 1971-2019.Relative to standard affine term structure models with stochastic volatility, the modelimproves the fit of yield volatility substantially, especially for long-maturity yields. Thisimprovement does not come at the expense of a deterioration in yield fit. We concludethat the ability of no-arbitrage term structure models to extract and model conditionalvolatility critically depends on the specification of the volatility factors. Modeling volatilityas a function of (lagged) squared innovations to factors improves on models where volatilityis a linear function of the factors