They are a way of solving probabilistic problems through simulating many scenarios of the given problem. Helpful for finding expected value, variance, and other numerical summaries for complex problems. Learn more here: https://en.wikipedia.org/wiki/Monte_Carlo_method
For this project, we are simulating Financial Derivatives. Why? Options are complex and hard to simulate using analytical formulas. This is usually done with risk-neutral pricing (since it's easier to calculate)
- Variance reduction methods:
- Antithetic variates
- Control variates
- Quasi-random variates compared to pseudo random numbers