Unspanned Stochastic Volatility in the Linear-Rational Square-Root Model: Evidence from the Treasury Market *

Abstract

We examine the linear-rational square-root (LRSQ) models' ability to capture crosssectional and time-series dynamics of bond yields and their variances simultaneously. The preferred model specification has five factors, two of which are not spanned by the yield curve, introducing unspanned stochastic volatility (USV). This specification provides a close in-sample fit to yields and yield variances, emphasizing the need of USV. Out-of-sample, it demonstrates low variance forecast errors. Additionally, the model provides evidence of USV in conditional yield variance and bond risk premia, which is linked to macroeconomic uncertainty.

Keywords: Interest rate model, Treasury market, Unscented Kalman filter, Unspanned stochastic volatility, Unspanned risk premia JEL Classification: C32, G12, E43

JEL Classification: C32, G12, E43