NonParametric Estimation Of Diffusion Coefficient: An Empirical Evidence using Option Pricing on S&P 500

In this paper, we discuss the estimation of the di usion coe cient of an Itô process fromhigh-frequency data using a nonparametric approach by Nadayara-Watson estimator. The principal purpose is to estimate the di usion coe cient using selective estimators of spot volatility proposed by several authors, which are based on the observed trajectories. In general, statistical and econometrical criteria are used for comparing spot volatility estimators used in nonparametric estimators. We want to resort to merely nancial metrics to achieve the same task. More precisely, the accuracy of di erent spot volatility estimates is measured in terms of how accurately they can reproduce market option prices. The model is implemented using S&P 500 data, and successively, we used it to estimate european call option prices written on the S&P 500 index. The estimation results are compared to well-known parametric alternative available in the literature. Empirical results not only provide strong evidence that most traditional pricing model are mispeci ed, but also con rm that the nonparametric model generates signi cantly di erent prices of common derivatives.