Quadratic Term Structure Models: Theory and Evidence

Dong-Hyun Ahn, Robert F. Dittmar, and A. Ronald Gallant
The Review of Financial Studies Vol. 15, Issue 1, Spring 2002, 243-288 .


This paper theoretically explores the characteristics underpinning quadratic term structure models (QTSMs), which designate the yield on a bond as a quadratic function of underlying state variables. We develop a comprehensive QTSM, which is maximally flexible and thus encompasses the features of several diverse models including the double square-root model of Longstaff (1989), the univariate quadratic model of Beaglehold and Tenney (1992), and the Squared-Autoregressive-Independent-Variable Nominal Term Structure (SAINTS) model of Constantinides (1992). We document a complete classification of admissibility and empirical identification for the QTSM, and demonstrate that the QTSM can overcome limitations inherent in affine term structure models (ATSMs). Using the Efficient Method of Moments of Gallant and Tauchen (1996), we test the empirical performance of the model in determining bond prices and compare the performance to the ATSMs. The results of the goodness-of-fit tests suggest that the QTSMs outperform the ATSMs in explaining historical bond price behavior in the US.