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

Abstract

This study examines the ability of the linear-rational square-root model to simultaneously capture cross-sectional and time-series dynamics of bond yields and their variances. The preferred model specification comprises 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 for USV. Out-of-sample testing demonstrates low variance forecast errors. The specification provides evidence of USV in conditional yield variance and bond risk premia, 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