Nonparametric methods for volatility density estimation

Stochastic volatility modelling of financial processes has become increasingly popular. The proposed models usually contain a stationary volatility process. We will motivate and review several nonparametric methods for estimation of the density of the volatility process. Both models based on discretely sampled continuous time processes and discrete time models will be discussed. The key insight for the analysis is a transformation of the volatility density estimation problem to a deconvolution model for which standard methods exist. Three type of nonparametric density estimators are reviewed: the Fourier-type deconvolution kernel density estimator, a wavelet deconvolution density estimator and a penalized projection estimator. The performance of these estimators will be compared. Key words: stochastic volatility models, deconvolution, density estimation, kernel estimator, wavelets, minimum contrast estimation, mixing