Monte Carlo simulation is named after the famous casino in the principality of Monaco. It is the most widely used numerical method to price financial derivatives in the industry because of its simplicity, flexibility, and extensibility.
The basic idea of the method is to construct a simulation engine that will allow us to predict a number of possible ways (or trajectories) in which the underlying assets can evolve in the future. These trajectories can be thought of as potential economic or financial scenarios. With MC simulation, we attempt to answer questions such as "given the observed price of Vodafone stock today, what could be the likely prices of the stock each day for the next month?"
As we cannot be certain of the future evolution of prices, our result needs to be based on probability, and, thus, we need large number of samples. Using the stochastic models that we saw in the previous chapter to simulate one possible trajectory, with MC simulation,...