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, mixin
