I simulated sample paths to approximate the price of a vanilla European call and then plotted a graph comparing this to the value achieved from the Black Scholes. Why do these values diverge as the option volatility increases?
Each path is evolved based on the vol and a random number. The higher the vol the more the paths will diverge.
Paths will diverge if you increase time as well.
The solution is to increase the number of paths as vol or time increases to get a standard deviation of terminal values that you are comfortable with.