Abstract :
In this paper, new fully nonparametric estimators of the diffusion coefficient of
continuous time models are introduced+ The estimators are based on Fourier analysis
of the state variable trajectory observed and on the estimation of quadratic
variation between observations by means of realized volatility+ The estimators proposed
are shown to be consistent and asymptotically normally distributed+ Moreover,
the Fourier estimator can be iterated to get a fully nonparametric estimate
of the diffusion coefficient in a bivariate model in which one state variable is the
volatility of the other+ The estimators are shown to be unbiased in small samples
using Monte Carlo simulations and are used to estimate univariate and bivariate
models for interest rates+
