Chapter 37: How Volatility Affects Popular Strategies 779 
Example: Suppose that XYZ is trading at 100, and one is interested in a calendar 
spread in which an August (5-month) call is bought and a May (2-month) call is sold. 
For the purpose of this example, it will be assumed that these are both at-the-money 
options. First, the vegas of the two options will be examined, assuming that implied 
volatility is 40%: 
Stock: 100 
Implied Volatility: 
40% Option 
Sell May 100 call 
Buy August 1 00 call 
Theoretical Price 
6.91 
11.22 
Vega 
0.162 
0.251 
In theory, this spread should be worth 4.31 - the difference in the theoretical 
values. Perhaps more important, it has volatility exposure of 0.089 - the difference 
between the vega of the long call and that of the short call. Since vega is positive, this 
means that an increase in implied volatility will be beneficial to the spread. In other 
words, one can expect the spread to widen if implied volatility rises, and can expect 
the spread to shrink if implied volatility declines. 
The following table can also be constructed, showing the theoretical value of 
the spread at various levels of implied volatility. This table makes the assumption that 
very little time has passed ( only one week) before the implied volatility changes take 
place. It also assumes that the stock is still at 100. 
Stock Price: 100 
One week ofter the spread hos been established: 
Implied Volatility Theoretical Spread Value 
20% 2.58 
30% 3.52 
40% 4.46 
50% 5.40 
60% 6.33 
80% 8.16 
100% 12.92 
From the above data, it is quite obvious that implied volatility levels have a huge 
effect on the value of a calendar spread. The actual initial contribution of time decay 
is rather small in comparison. For example, note that if volatility remains unchanged 
at 40%, then the spread will have widened only slightly - to 4.46 from 4.31 - after 
the passage of one week's time. That is small in comparison to the changes dictated 
by volatility expansion or contraction.