Empirical Study on the Performances of Black-Scholes Model for Evaluating European Options

In this study we aim at analyzing the way the model Black-Scholes works in practice.
The data used for analysis refer to European-type call options having as supportassets the CAC-40 money-market index. Our approach will be structured in two parts.
The first will be dedicated to an estimate of daily implicit volatilities, which is of those values of volatilities which, once applied in the Black-Scholes evaluation formula, minimize the sum of square errors given by the model. Once this problem is solved, we
will analyze the relationship existing between implicit volatility moneyness and due term of options, that is the so-called volatility smile. The second part of the study will have as core the analysis of errors provided by the Black-Scholes model, which will be studied, given moneyness and due-term of options.