Approximating Volatility Diffusions with CEV-ARCH Models

Abstract

Aim of this article is to judge the empirical performance of Arch as diffusion approximations to models of the short-term rate with stochastic volatility and as filters of the unobserved volatility. We show that the estimation of the continuous time scheme to which a discrete time Arch model converges can be safely based on simple moment conditions linking the discrete time to the continuous time coefficients. A natural substitute of a global specification test for just-identified problems based on indirect inference shows in fact that this approximation to diffusions gives rise to a negligible disaggregation bias. Unlike previous literature in which standard Arch models approximated only specific diffusions, our estimation strategy relies on a new Arch model that approximates any CEV-diffusion model for the conditional volatility. A Monte-Carlo study reveals that the filtering performances of this model are remarkably good, even in the presence of an important kind of misspecification.