Project on numerical methods : a proof on Monte Carlo method to price European options

Abstract

In this project we show how European options can be priced by using the Monte Carlo method. Since the first results were positive, assuming that market is following Black-Scholes model, we saw how the value estimated with the Monte Carlo method was becoming closer to the real value of the model. Thus, we were asked to design a new option: APE; and estimate its price by implementing the Monte Carlo method seen in the procedure used in first section of the project. In conclusion, results were becoming closer to real values by increasing the number of observations done and the tries made; therefore Monte Carlo Method has been checked and we determine that it can be very useful to estimate value of all these new options.