Quadratic Term Structure Models: Theory and Evidence

• Published in: The Review of financial studies Vol. 15; no. 1; pp. 243 - 288
• Main Authors: Ahn, Dong-Hyun, Dittmar, Robert F., Gallant, A. Ronald
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 2002; Oxford Publishing Limited (England)
• Subjects: Bonds; Correlations; Covariance matrices; Economic models; Finance; Financial performance; Financial risk; Interest rates; Market prices; Mathematical models; Modeling; Nominal interest rates; Parametric models; Prices; Stock prices; Stock returns; Studies; Variable interest rates
• ISSN: 0893-9454; 1465-7368
• DOI: 10.1093/rfs/15.1.243

This article 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 Beaglehole 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 United States.