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.