Modeling the conditional mean and variance of the short rate using diffusion, GARCH, and moving average models

Abstract

This article introduces a two‐factor‐discrete‐time‐stochastic‐volatility model that allows for departures from linearity in the conditional mean and incorporates serially correlated unexpected news, asymmetry, and level effects into the definition of conditional volatility of the short rate. The new class of econometric specifications nests many popular existing symmetric and asymmetric GARCH as well as diffusion models of the short‐term interest rate. This study attempts to determine the correct specification of conditional mean and variance of the short rate by developing a more general econometric framework that allows for nonlinear effects in the drift of the short rate, and that defines the conditional volatility as a nonlinear function of unexpected information shocks and interest rate levels. The existing and alternative models are compared in terms of their ability to capture the stochastic behavior of the short‐term riskless rate. The empirical results indicate that the relative performance of the two‐factor models in predicting the future level and variance of interest‐rate changes is superior to the nested models. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:717–751, 2000