32  •   The Intelligent Option Investor
This example illustrates precisely the process on which the BSM and 
all other statistically based option pricing formulas work. The BSM has a 
fixed number of inputs regarding the underlying asset and the contract itself. 
Inputting these variables into the BSM generates a range of likely future values 
for the price of the underlying security and for the statistical probability of the 
security reaching each price. The statistical probability of the security reach-
ing a certain price (that certain price being a strike price at which we are inter-
ested in buying or selling an option) is directly tied to the value of the option.
Now that you have a feel for the BSM on a conceptual dining-
reservation level, let’s dig into a specific stock-related example.
Step-by-Step Method for Predicting Future Stock 
Price Ranges—BSM-Style
In order to understand the process by which the BSM generates stock price 
predictions, we should first look at the assumptions underlying the model. 
We will investigate the assumptions, their tested veracity, and their impli-
cations in Chapter 3, but first let us just accept at face value what Messrs. 
Black, Scholes, and Merton take as axiomatic.
According to the BSM,
• Securities markets are “efficient” in that market prices perfectly 
reflect all publicly available information about the securities. This 
implies that the current market price of a stock represents its fair 
value. New information regarding the securities is equally likely to 
be positive as negative; as such, asset prices are as likely to move up 
as they are to move down.
• Stock prices drift upward over time. This drift cannot exceed the 
risk-free rate of return or arbitrage opportunities will be available.
• Asset price movements are random and their percentage returns 
follow a normal (Gaussian) distribution.
• There are no restrictions on short selling, and all hedgers can bor -
row at the risk-free rate. There are no transaction costs or taxes. 
Trading never closes (24/7), and stock prices are mathematically 
continuous (i.e., they never gap up or down), arbitrage opportuni-
ties cannot persist, and you can trade infinitely small increments of 
shares at infinitely small increments of prices.