Purebred or Hybrid : Reproducing the Volatility in Term Structure Dynamics

This paper investigates the implications of mixtures of affine, quadratic, and nonlinear models for the term structure of volatility. The dynamics of the term structure of interest rates appear to exhibit pronounced time-varying or stochastic volatility. Ahn, Dittmar, and Gallant (2000) provide evidence suggesting that term structure models incorporating a set of quadratic state variables are better able to reproduce yield dynamics than affine models, though none of the models is able to fully capture the term structure of volatility. In this study, we combine affine, quadratic and nonlinear factors in order to maximize the strengths of a term structure model in generating heteroskedastic volatility. We show that this combination entails a tradeoff between specification of heteroskedastic volatility and correlations among the state variables. By combining these factors, we are able to gauge the cost of this tradeoff. Using the Efficient Method of Moments [Gallant and Tauchen (1996)], we find that augmenting a quadratic model with a nonlinear factor results in improvement in fit over a model characterized only by quadratic factors. Since the nonlinear factor is characterized by stronger dependence of volatility on the level of the factor, we conclude that flexibility in the specification of both level dependence and correlation structure are important for describing term structure dynamics