We consider a continuous-time stochastic volatility model. The model contains a stationary volatility process, the density of which, at a fixed instant in time, we aim to estimate. We assume that we observe the process at discrete instants in time. The sampling times will be equidistant with vanishing distance. A Fourier-type deconvolution kernel density estimator based on the logarithm of the squared processes is proposed to estimate the volatility density. An expansion of the bias and a bound on the variance are derived.
"Nonparametric volatility density estimation." Bernoulli 9 (3) 451 - 465, June 2003. https://doi.org/10.3150/bj/1065444813