Chapter 40: Advanced Concepts 849 
Let us now take a look at how both volatility and time affect the delta of a call 
option. Much of the data to be presented in this chapter will be in both tabular and 
graphical form, since some readers prefer one style or the other. 
The volatility of the underlying stock has an effect on delta. If the stock is not 
volatile, then in-the-money options have a higher delta, and out-of-the-money 
options have a lower delta. Figure 40-1 and Table 40-1 depict the deltas of various 
calls on two stocks with differing volatilities. The deltas are shown for various strike 
prices, with the time remaining to expiration equal to 3 months and the underlying 
stock at a price of 50 in all cases. Note that the graph confirms the fact that a low­
volatility stock's in-the-money options have the higher delta. The opposite holds true 
for out-of-the-money options: The high-volatility stock's options have the higher delta 
in that case. Another way to view this data is that a higher-volatility stock's options will 
always have more time value premium than the low-volatility stock's. In-the-money, 
these options with more time value will not track the underlying stock price move­
ment as closely as ones with little or no time value. Thus, in-the-money, the low­
volatility stock's options have the higher delta, since they track the underlying stock 
price movements more closely. Out-of-the-money, the entire price of the option is 
composed of time value premium. The ones with higher time value (the ones on the 
high-volatility stock) will move more since they have a higher price. Thus, out-of-the­
money, the higher-volatility stock's options have the greater delta. 
Time also affects delta. Figures 40-2 (see Table 40-2) and 40-4 show the rela­
tionships between time and delta. Figure 40-2's scales are similar to those in Figure 
40-2, delta vs. volatility: The deltas are shown for various striking prices, with XYZ 
assumed to be equal to 50 in all cases. Notice that in-the-money, the shorter-term 
options have the higher delta. Again, this is because they have the least time value 
premium. Out-of-the-money, the opposite is true: The longer-term options have the 
higher deltas, since these options have the most time value premium. 
Figure 40-3 (see Table 40-3) depicts the delta for an XYZ January 50 call with 
XYZ equal to 50. The horizontal axis in this graph is "weeks until expiration." Note 
that the delta of a longer-term at-the-money option is larger than that of a shorter­
term option. In fact, the delta shrinks more rapidly as expiration draws nearer. Thus, 
even if a stock remains unchanged and its volatility is constant, the delta of its options 
will be altered as time passes. This is an important point to note for the strategist, 
since he is constantly monitoring the risk characteristics of his position. He cannot 
assume that his position is the same just because the stock has remained at the same 
price for a period of time. 
Position Delta. Another usage of the term delta is what has previously been 
referred to as the equivalent stock position (ESP); for futures options, it would be