In this first example, we consider the pricing of a plain vanilla European Call option. This example is exceedingly simple but crucial; it will serve as the building block for the rest of the option pricing problems to be solved with the Monte Carlo simulation.
The full characteristics of the contract, the choice of the mathematical model, and its numerical method are shown below in the Bento Box template:
Our objective is to calculate the premium of this financial derivative. We proceed by completing the contents of the Bento Box in clockwise sense, starting from the top-left corner. We first fill all the data of the contract, in particular the payoff function, which for a simple European Call is as follows:
Secondly, we ought to select the mathematical model for the underlying, which in the case of equities is GBM. Third, we select the numerical method to be used as Monte Carlo simulation. Fourth, we construct...