Discrete-Time Affine Term Structure Models : An ARCH Formulation

Discrete-time Affine Term Structure Models can be expressed in AR(1)- ARCH form, but it is not possible to get a non-negative variance equation only by restricting the parameters. In this paper we use a distribution assumption in order to assure the variance to be non-negative. We present a complete formulation for one-factor and multi-factor models with Inverse Gaussian conditional innovations distribution. Moreover, we derive the log-likelihood functions and implement a two-factor empirical specification analysis both with simulated and US interest rate data. We compare the estimation and forecasting results with an AR(1)-GARCH(1,1) model