Keywords: ARCH, discrete-time ATSM, affine term structure models, maximum likelihood estimation, VAR, interest rates, financial risk
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 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 a AR(1)-GARCH(1,1) model.