An introduction to the mathematical cornerstone of financial derivatives

Abstract

[en] There are several paths that lead to the Black-Scholes formula. This project discusses two of them. Chapters 2 and 3 depart from the discrete Cox-Ross-Rubinstein model of prices and reveal the Black-Scholes formula for European calls and puts. Chapters 4 and 5 go one step further by considering since inception the continuous modelling of prices, in which a new concept of integral must be defined in order to formulate the Black-Scholes hypotheses from a stochastical point of view. The project ends up debating the uses of derivatives and the appropriateness of the Black-Scholes model in the real world. Moreover, the annex contains Numerical Methods that implement the models covered in this project.