|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.