Chapter 28: Mathematical Applications 489 
information on the underlying stock are also necessary. The larger programmable cal­
culators can handle calculations such as the Black-Scholes model, computing the 
hedge ratio, and determining the probability of a stock being above or below a cer­
tain price at some future time. However, more involved calculations, such as com­
puting the implied volatility or determining the expected return of a position, require 
the use of a computer. 
SUMMARY 
Two basic mathematical aids have been presented: the pricing model and the ability 
to predict the probability of a stock's movement. The hedge ratio and the expected 
return analysis are extensions of the basic aids. Any strategy can be evaluated with 
these tools. Such an analysis should be able to give the trader or strategist some idea 
of the relative attractiveness of establishing the position, and may also aid in making 
follow-up adjustments to the position. All the analyses rely heavily on one's estimate 
of the volatility of the underlying stock Using the implied volatility seems to be one 
of the best ways to obtain an accurate, current volatility estimate, since it is derived 
from the prices in the market itself. The applications presented here are not all-inclu­
sive. The strategist who is, or becomes, familiar with the advantages of rigorous math­
ematical analysis will be able to construct many other aids for his trading that utilize 
the basic mathematics described in this chapter.