October 2023
Intermediate to advanced
640 pages
16h 23m
English
Peter McQuire
In this chapter we develop, starting with the simple random walk, one of the most widely used models for projecting future share prices – Geometric Brownian Motion (“GBM”). To see where we are aiming, we have set out below, with no explanation at this point, the discrete time approximation of GBM, where
is the stock price at time
:
which is exact as
. Using the rules of stochastic calculus, we arrive at the exact solution for the price
at time
:
where
is the expected rate of return per unit time from the stock, is the standard deviation of the returns from the ...