A comparative analysis of nonparametric volatility estimators: an empirical evidence using option pricing on standard and poor's 500

This thesis studies the efficiency of some estimators of the spot and integrated volatilities proposed in the recent literature and uses high frequency data. It is well known that financial high frequency data evidence microstructure effects which render the classics estimator of the volatility inappropriate, namely the “realized volatility”. Therefore, it is necessary to use volatility estimate which is robust in the presence of those effects. The dissertation examines some of those estimates comparing their performance first using statistic-econometrics technics and successively with pure financial criteria or in term of their ability for working out the price of options written on the S&P 500. Precisely, the use of the studied estimators of the spot volatilty permits by means of a Nadayara and Watson regression type, of estimating the functional form of the diffusion coefficient in a local volatility model and we successively used it for the pricing of the derivative with Dupire's equation. This approach is based on the estimation of the underlying asset which is different from the classical technics of derivatives pricing based exclusively on the PDE (partial differencial equation). Furthermore, this allows to take into account high information available in the high frequency data contained in the underlying asset which are generally neglected and can be of higher interest when pricing “out of the money” options or when less information is available for options similar to those we want to evaluate. The principal contributions of this article are: firstly, the study of the consistency and asymptotically normally distribution fo the errors for the new proposed estimators, secondly, the comparison of diffeerent estimators of the spot volatility in term of option pricing. Finally, we have compared the result of this approach with those of classical (parametric) approach obtained by PDE, and successively, with the prices estimated using only daily data (low frequency).