Title: A non-parametric estimator for stochastic volatility density

Authors: Soufiane Ouamaliche; Awatef Sayah

Addresses: Laboratory of Mathematics, Computing and Applications – Information Security, Faculty of Sciences, Mohammed V University, BP1014RP, Rabat, Morocco ' Laboratory of Mathematics, Computing and Applications – Information Security, Faculty of Sciences, Mohammed V University, BP1014RP, Rabat, Morocco

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 (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.

Keywords: non-parametric estimation; kernel smoothing; kernel regression; kernel density estimation; convolution structure; stochastic volatility; Monte Carlo simulations.

DOI: 10.1504/IJCEE.2021.118476

International Journal of Computational Economics and Econometrics, 2021 Vol.11 No.4, pp.349 - 367

Accepted: 08 May 2020
Published online: 27 Oct 2021 *

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