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 (Y-t, V-t) such that only (Y-t) is an observable coordinate. Polynomials of different degrees are then adjusted using weighted least squares to filter the observations of the variance coordinate (V-t) 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.