NONPARAMETRIC ESTIMATION OF THE DIFFUSION COEFFICIENT OF STOCHASTIC VOLATILITY MODELS

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+