A non-parametric estimator for stochastic volatility density

This paper aims at improving the accuracy of stochastic volatility density estimation in a high frequency setting using a simple procedure involving a combination of kernel smoothing methods namely, kernel regression and kernel density estimation. The employed data, which are 30 years worth of hourly observations, are simulated through a constant elasticity of variance-stochastic volatility (CEV-SV) model, namely the Heston model, calibrated to fit the S%P 500 Index, in the form of a two-dimensional diffusion process (Yt, Vt) such that only (Yt) is an observable coordinate. Polynomials of different degrees are then adjusted using weighted least squares to filter the observations of the variance coordinate (Vt) from a convolution structure before applying a straightforward kernel density estimation. The obtained estimates did well when compared to previous results as they have displayed a certain improvement, linked to the degree of the fitted polynomial, by reducing the value of the mean integrated squared error (MISE) criterion computed with respect to a benchmark density suggested in the literature.