Summary

In this chapter, we applied the concepts of simulation based on Monte Carlo methods and, more generally, on the generation of random numbers to real cases related to the world of financial engineering. We started by defining the model based on Brownian motion, which describes the uninterrupted and irregular movement of small particles when immersed in a fluid. We learned how to describe the mathematical model, and then we derived a practical application that simulates a random walk as a Wiener process.

Afterward, we dealt with another practical case of considerable interest, that is, how to use Monte Carlo methods to predict the stock prices of the famous Amazon company. We started to explore the trend of Amazon sharess in the last 10 years, and we performed simple statistics to extract preliminary information on any trends that we confirmed through visual analysis. Subsequently, we learned to treat the trend of stock prices as a time series, calculating the daily return...