Quadratic Term Structure Models: Theory and Evidence

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. Copyright 2002, Oxford University Press.

[1]  Oldrich A. Vasicek.  An equilibrium characterization of the term structure , 1977 .

[2]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[3]  M. David.  HARRISON, J. Michael, and KREPS, . Martingales and Arbitrage in Multiperiod Securities Markets, Journal of Economic Theory, , . , 1979 .

[4]  David M. Kreps,et al.  Martingales and arbitrage in multiperiod securities markets , 1979 .

[5]  T. C. Langetieg.  A Multivariate Model of the Term Structure , 1980 .

[6]  J. Harrison,et al.  Martingales and stochastic integrals in the theory of continuous trading , 1981 .

[7]  S. Ross,et al.  AN INTERTEMPORAL GENERAL EQUILIBRIUM MODEL OF ASSET PRICES , 1985 .

[8]  S. Ross,et al.  A theory of the term structure of interest rates'', Econometrica 53, 385-407 , 1985 .

[9]  Ioannis Karatzas,et al.  Brownian Motion and Stochastic Calculus , 1987 .

[10]  Lars Peter Hansen,et al.  THE ROLE OF CONDITIONING INFORMATION IN DEDUCING TESTABLE RESTRICTIONS IMPLIED BY DYNAMIC ASSET PRICING MODELS1 , 1987 .

[11]  A. Gallant,et al.  Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications , 1989 .

[12]  Francis A. Longstaff,et al.  A nonlinear general equilibrium model of the term structure of interest rates , 1989 .

[13]  D. Beaglehole,et al.  General Solutions of Some Interest Rate-Contingent Claim Pricing Equations , 1991 .

[14]  Corrections and additions to ‘a nonlinear equilibrium model of the term structure of interest rates’ , 1992 .

[15]  Eduardo S. Schwartz,et al.  Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model , 1992 .

[16]  Tong-sheng Sun,et al.  Real and Nominal Interest Rates: A Discrete-Time Model and Its Continuous-Time Limit , 1992 .

[17]  Ren-Raw Chen,et al.  Pricing Interest Rate Options in a Two-Factor Cox–Ingersoll–Ross model of the Term Structure , 1992 .

[18]  G. Constantinides.  A Theory of the Nominal Term Structure of Interest Rates , 1992 .

[19]  J. Huston McCulloch,et al.  U.S. term structure data, 1947-1991 , 1993 .

[20]  Robert B. Litterman,et al.  Explorations into Factors Explaining Money Market Returns , 1994 .

[21]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[22]  A. Gallant,et al.  Which Moments to Match? , 1995, Econometric Theory.

[23]  Yacine Ait-Sahalia.  Testing Continuous-Time Models of the Spot Interest Rate , 1995 .

[24]  George Tauchen,et al.  SNP: A Program for Nonparametric Time Series Analysis. Version 8.4. User's Guide , 1995 .

[25]  Narasimhan Jegadeesh,et al.  The Behavior of Interest Rates Implied by the Term Structure of Eurodollar Futures , 1996 .

[26]  S. Claessens,et al.  Estimating the Likelihood of Mexican Default from the Market Prices of Brady Bonds , 1996, Journal of Financial and Quantitative Analysis.

[27]  D. Duffie,et al.  A YIELD-FACTOR MODEL OF INTEREST RATES , 1996 .

[28]  R. Sundaram,et al.  A Simple Approach to Three-Factor Affine Term Structure Models , 1996 .

[29]  Yacine Aït-Sahalia.  Nonparametric Pricing of Interest Rate Derivative Securities , 1996 .

[30]  A Three-Factor Model of the Term Structure of Interest Rates , 1996 .

[31]  T. Andersen,et al.  Estimating continuous-time stochastic volatility models of the short-term interest rate , 1997 .

[32]  D. Duffie,et al.  An Econometric Model of the Term Structure of Interest-Rate Swap Yields , 1997 .

[33]  A. Gallant,et al.  Estimating stochastic differential equations efficiently by minimum chi-squared , 1997 .

[34]  K. Singleton,et al.  Specification Analysis of Affine Term Structure Models , 1997 .

[35]  Richard Stanton.  A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk , 1997 .

[36]  Neil D. Pearson,et al.  Is the Short Rate Drift Actually Nonlinear , 2000 .

[37]  A. Gallant,et al.  Reprojecting Partially Observed Systems with Application to Interest Rate Diffusions , 1998 .

[38]  Neil D. Pearson,et al.  Using Proxies for the Short Rate: When Are Three Months Like an Instant? , 1999 .

[39]  Biao Lu.  An Empirical Analysis of the Constantinides Model of the Term Structure ¤ , 1999 .

[40]  D. Ahn,et al.  A Parametric Nonlinear Model of Term Structure Dynamics , 1999 .

[41]  K. Singleton,et al.  Expectation puzzles, time-varying risk premia, and affine models of the term structure , 2002 .

[42]  G. Duffee.  Term premia and interest rate forecasts in affine models , 2000 .