A Semiparametric Two-Factor Term Structure Model

This article proposes a semiparametric two-factor term structure model based on a consol rate and the spread between a short rate and the consol rate. The diffusion functions in both the consol rate and spread processes are nonparametrically specified so that the model allows for maximal flexibility of diffusion functions in fitting into data. The drift function of the spread process is specified as a mean-reverting function, while the drift function of the consol rate process is left unrestricted. A nonparametric procedure is developed for estimating the diffusion functions. The asymptotic biases of the nonparametric estimators are quantified when the step of discretization is fixed, while the asymptotic distributions of the nonparametric estimators are derived when the step of discretization tends to zero. The pricing and hedging performances of the model are evaluated in a simulated economic environment. Results show that the model performs quite well in the simulated economy