Modeling Volatility in Dynamic Term Structure Models

Abstract

We propose no-arbitrage term structure models in which the volatility factors follow
GARCH processes. The models’ tractability is similar to that of canonical affine term
structure 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 model
improves the fit of yield volatility substantially, especially for long-maturity yields. This
improvement does not come at the expense of a deterioration in yield fit. We conclude
that the ability of no-arbitrage term structure models to extract and model conditional
volatility critically depends on the specification of the volatility factors. Modeling volatility
as a function of (lagged) squared innovations to factors improves on models where volatility
is a linear function of the factors.

Keywords: term structure; stochastic volatility; GARCH.

JEL Classification: G12, C58, E43