Vanilla Equity Options and Greeks Revisited

Today there are many equity derivatives that are traded on organized and over-the-counter markets. The models that allow market participants to value them and manage the associated risks on a daily basis are numerous. The idea of this study is, for vanilla equity options, to understand the Black and Scholes model which is the most commonly used model in the matter and confront it with reality. We will therefore begin by recalling known results and then try to raise the problems that are encountered when attempting to apply them in a practical context