2002/02 LEM Working Paper Series

Which Model for the Italian Interest Rates?
M. Gentile, R. RenÚ
Estimation by simulation, method of moments, stochastic differential equations, diffusions, interest rate term structure, yield curve.

In the recent years, di usion models for interest rates became very pop- ular. In this paper, we try to do a selection of a suitable di usion model for the Italian interest rates. Our data set is given by the yields on three-month BOT, from 1981 to 2001, for a total of 470 observations. We investigate among stochastic volatil- ity models, paying more attention to a ne models. Estimating di usion models via maximum likelihood, which would lead to e ciency, is usually unfeasible since the transition density is not available. Recently it has been proposed a method of mo- ments which gains full e ciency, hence its name of E cient 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 di usions whose transition density is un- known, 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 which are easy to compute and to interpret. We nd evidence that one- factor models are rejected, while a logarithmic speci cation of the volatility provides the best t to the data, in agreement with the ndings on U.S. data. Moreover, we provide evidence that this model allows a more exible representation of the yield curve.

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