Nonparametric volatility density estimation for discrete time models

We consider discrete time models for asset prices with a stationary volatility process. We aim at estimating the multivariate density of this process at a set of consecutive time instants. A Fourier-type deconvolution kernel density estimator based on the logarithm of the squared process is proposed to estimate the volatility density. Expansions of the bias and bounds on the variance are derived.