More Advanced Scenarios

Monte-Carlo simulation of terminal values is a relatively simple simulation, and one can probably be completed analytically. The true power of Monte-Carlo simulation is unlocked when analysing scenarios that are more difficult to solve analytically, if not impossible. For example, if we wanted to analyse an American-style option, which can be exercised anytime, we might want to count the probability of a stock price exceeding the strike price at any time during the lifetime of that option. We could do this by counting how many trials cross the strike price boundry.