A non-parametric estimator for stochastic volatility density. (31st August 2021)

• Record Type: Journal Article
• Authors: Ouamaliche, Soufiane; Sayah, Awatef
• Is Part Of: International journal of computational economics and econometrics. Volume 11:Number 4(2021)
• Page Start: 349
• Page End: 367
• Publication Date: 2021-08-31
• Subjects: non-parametric estimation -- kernel smoothing -- kernel regression -- kernel density estimation -- convolution structure -- stochastic volatility -- Monte Carlo simulations; Econometrics -- Periodicals; Economics -- Data processing -- Periodicals; 330.01519505
• Languages: English
• ISSNs: 1757-1170

Abstract

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.