Monte Carlo simulation in the context Financial Modeling refers to a set of
techniques to generate artificial time series of the stock price,volatility and interest rate and... overtime, from which option prices can be derived. There are several choices available in this regard. The first choice is to apply a standard method such as the Euler, Milstein, or implicit Milstein scheme, as described by Gatheral and Kahl and Jackel , for example. The advantage of these schemes is that they are easy to understand, and their convergence properties are famous.The other choice is to use a method that is better suited, or that is specifically designed for the especial models.These methods include quadratic-exponential scheme of Andersen , the transformed volatility scheme of Zhu , the scheme of Alfonsi,or the moment-matching scheme of Andersen,et al . These schemes are designed to have faster convergence to the true option price, and in some cases, to also avoid the negative variances that can sometimes be generated from standard methods. These and other schemes are reviewed by Van Haastrecht and Pelsser (2010).Also,to Valuing American option ,you can use the simulation-based algorithm of Longstaff and Schwartz.