Estimation of Stochastic Volatility Models by Nonparametric Filtering

A two-step estimation method of stochastic volatility models is proposed: In the first step, we estimate the (unobserved) instantaneous volatility process using the estimator of Kristensen (2010, Econometric Theory 26). In the second step, standard estimation methods for fully observed diffusion processes are employed, but with the filtered volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and we give theoretical results for both. The resulting estimators of the drift and diffusion terms of the volatility model will carry additional biases and variances due to the first-step estimation, but under regularity conditions these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties of the proposed estimators.