A Simple Approach to the Estimation of Continuous Time CEV Stochastic Volatility Models of the Short-Term Rate

Aim of this article is to judge the empirical performance of 'ARCH models as diffusion approximations' of models of the short-term rate with stochastic volatility. Our estimation strategy is based both on moment conditions needed to guarantee the convergence of the discrete time models and on the quasi indirect inference principle. Unlike previous literature in which standard ARCH models approximate only specific diffusion models (those in which the variance of volatility is proportional to the square of volatility), our estimation strategy relies on ARCH models that approximate any CEV-diffusion model for volatility. A MonteCarlo study reveals that the filtering performances of these models are remarkably good, even in the presence of important misspecification. Finally, based on a natural substitute of a global specification test for just-identified problems designed within indirect inference methods, we provide strong empirical evidence that approximating diffusions with our models gives rise to a disaggregation bias that is not significant.