In this chapter, we will show how to use the results of Chapter 20 to simulate geometric Brownian motion-based stock prices, first at a single point in time, and then along a whole path.
This is a very important chapter for practical financial modeling.
In Section 22.214.171.124, we showed, using Ito’s lemma, that the solution of the geometric Brownian motion stochastic differential equation
is available in closed form:
Since, if we use only information available at time 0 (at which time W0 = 0, Wt has zero mean, variance t, and is normally distributed), we can write this as