Here an introduction for my Master's Thesis for my Master's Degree in Mathematics and Computer Science at Imperial College, entitled, Variance Reduction Techniques For Monte Carlo Methods For Use In The Pricing of Exotic Options.

What are Monte Carlo Methods?

Say we want to know the probability of getting a six when we roll a die. The answer is obviously 1/6. However, alternatively we could roll a die many times and we'd find that approximately 1/6th of all rolls would produce a six. This is essentially what is at the core of Monte Carlo methods, simulating a process and then using an average to get an answer. In some cases getting analytical answers to such averages can be extremely difficult (sometimes impossible), in which case we have to resort to Monte Carlo methods (or other numerical techniques).