Monte Carlo Methods in Finance

Monte Carlo (MC) methods are vastly used to approximate the price of financial derivatives and the reasons which make them so popular are:

1. the curse of dimensionality when the derivative is on a bunch of assets which makes the deterministic numerical methods for PDEs useless,
2. the existence of non-Markovian exotic derivatives which makes the above technique in applicable.

The beginning of the MC in finance was the 1977 paper of Phelim Boyle:

Phelim Boyle, Options: A Monte Carlo Approach, Journal of Financial Economics (1977) 323-338

which has not any thing new in MC but the contribution is the application to derivative pricing. I suggest you to read the above paper and then follow the history of MC up to know. It is very interesting to see that from  the early work of Phelim up to present, some pure theories from stochastic process are born and maturated to cover financial demands to faster and more accurate methods e.g. backward stochastic differential equations or Malliavin approximation of conditional expectation. Does it at all excite you?

If you need a reference for MC, use the book of Paul Glasserman and if you need a faster and less detailed but complete enough text, use the Lecture Notes of Bruno Bouchard; of course with enough French proficiency.