Monte Carlo Simulations in Finance

Monte Carlo simulations are a class of computational algorithms that use repeated random sampling to solve any problems that have a probabilistic interpretation. In finance, one of the reasons they gained popularity is that they can be used to accurately estimate integrals. The main idea of Monte Carlo simulations is to produce a multitude of sample paths (possible scenarios/outcomes), often over a given period of time. The horizon is then split into a specified number of time steps and the process of doing so is called discretization. Its goal is to approximate the continuous time in which the pricing of financial instruments happens.

The results from all of these simulated sample paths can be used to calculate metrics such as the percentage of times an event occurred, the average value of an instrument at the last step, and so on. Historically, the main problem with the Monte Carlo approach was that it required heavy computational power to...