Purebred or hybrid? Reproducing the volatility in term structure dynamics

This paper investigates the ability of mixtures of affine, quadratic, and non-linear models to track the volatility in the term structure of interest rates. Term structure dynamics appear to exhibit pronounced time varying or stochastic volatility. Ahn et al. (Rev. Financial Stud. xx (2001) xxx) provide evidence suggesting that term structure models incorporating a set of quadratic factors are better able to reproduce term structure dynamics than affine models, although neither class of models is able to fully capture term structure volatility. In this study, we combine affine, quadratic and non-linear factors in order to maximize the ability of a term structure model to generate heteroskedastic volatility. We show that this combination entails a tradeoff between specification of heteroskedastic volatility and correlations among the factors. By combining factors, we are able to gauge the cost of this tradeoff. Using efficient method of moments (Gallant and Tauchen, Econometric Theory 12 (1996) 657), we find that augmenting a quadratic model with a non-linear factor results in improvement in fit over a model comprised solely of quadratic factors when the model only has to confront first and second moment dynamics. When the full dynamics are confronted, this result reverses. Since the non-linear 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 of the factors are important for describing term structure dynamics.