CHAPTER 28 
Mathetnatical Applications 
In previous chapters, many references have been made to the possibility of applying 
mathematical techniques to option strategies. Those techniques are developed in this 
chapter. Although the average investor - public, institutional, or floor trader - nor­
mally has a limited grasp of advanced mathematics, the information in this chapter 
should still prove useful. It will allow the investor to see what sorts of strategy deci­
sions could be aided by the use of mathematics. It will allow the investor to evaluate 
techniques of an information service. Additionally, if the investor is contemplating 
hiring someone knowledgeable in mathematics to do work for him, the information 
to be presented may be useful as a focal point for the work. The investor who does 
have a knowledge of mathematics and also has access to a computer will be able to 
directly use the techniques in this chapter. 
THE BLACK-SCHOLES MODEL 
Since an option's price is the function of stock price, striking price, volatility, time to 
expiration, and short-term interest rates, it is logical that a formula could be drawn 
up to calculate option prices from these variables. Many models have been conceived 
since listed options began trading in 1973. Many of these have been attempts to 
improve on one of the first models introduced, the Black-Scholes model. This model 
was introduced in early 1973, very near the time when listed options began trading. 
It was made public at that time and, as a result, gained a rather large number of 
adherents. The formula is rather easy to use in that the equations are short and the 
number of variables is small. 
The actual formula is: 
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