12. Monte Carlo Simulation

q. explain Monte Carlo simulation and describe its applications and limitations;

## r. compare Monte Carlo simulation and historical simulation.

What is a Monte Carlo Simulation? Monte Carlo simulation involves trying to simulate the conditions that apply to a specific problem by generating a large number of random samples using a random number generator on a computer.

Where does the name “Monte Carlo simulation” derive from? It comes from the idea of generating a large number of random samples, such as might occur in the Monte Carlo Casino.

What is the Monte Carlo simulation used for? - It allows us to experiment with a proposed policy and assess the risks before actually implementing it. - It is used to develop Value at Risk (VAR) to estimate the probability that portfolio losses exceed a predefined level. - It is used to value complex securities such as European options and mortgage-backed securities with complex embedded options - Researchers use it to test their models and tools

How are numbers generally picked for the Monte Carlo Simulation? Generally, a historical record of returns (or other underlying variables) are used because they provide direct evidence of distributions. A drawback is that any outcome which is not in the historical (such as a stock market crash or black swan events) will not be included.