Chapter 21
Simulating Geometric Brownian Motion
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.
21.1 Simulating GBM Stock Prices at a Single Future Time
In Section 20.3.5.2, 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
where ...
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