Specification Analysis of Diffusion Models for the Italian Short Rate

In recent years, diffusion models for interest rates became very popular. In this paper, we perform a selection of a suitable diffusion model for the Italian short rate. Our data set is given by the yields on 3‐month BOT (Buoni Ordinari del Tesoro), from 1981 to 2001, for a total of 470 observations. We investigate among stochastic volatility models, paying more attention to affine models. Estimating diffusion models via maximum likelihood, which would lead to efficiency, is usually unfeasible because the transition density is not available. Recently, Gallant and Tauchen (1996) proposed a method of moments which gains full efficiency, hence its name of Efficient Method of Moments (EMM); it selects the moments as the scores of an auxiliary model, to be computed via simulation; thus, EMM is suitable to diffusions whose transition density is unknown, but which are convenient to simulate. The auxiliary model is selected among a family of densities which spans the density space. As a by‐product, EMM provides diagnostics that are easy to compute and interpret. We find evidence that one‐factor models and multi‐factor affine models are rejected, while a logarithmic specification of the volatility provides the best fit to the data.