862 Part VI: Measuring and Trading Volatility 
of-the-money option will not be affected much by a change in volatility. In addition, 
for at-the-money options, longer-term options have a higher vega than short-term 
options. To verify this, think of it in the extreme: An at-the-money option with one 
day to expiration will not be overly affected by any change in volatility, due to its 
pending expiration. However, a three-month at-the-money option will certainly be 
sensitive to changes in volatility. 
Vega does not directly correlate with either delta or gamma. One could have a 
position with no delta and no gamma (delta neutral and gamma neutral) and still have 
exposure to volatility. This does not mean that such a position would be undesirable; 
it merely means that if one had such a position, he would have removed most of the 
market risk from his position and would be concerned only with volatility risk. 
In later sections, the use of volatility to establish positions and the use of vega 
to monitor them will be discussed. 
THETA 
Theta measures the time decay of a position. All option traders know that time is the 
enemy of the option holder, and it is the friend of the option writer. Theta is the name 
given to the risk measurement of time in one's position. Theta is generally expressed 
as a negative number, and it is expressed as the amount by which the option value 
will change. Thus, if an option has a theta of -0.12, that means the option will lose 
12 cents, or about an eighth of a point, per day. This is true for both puts and calls, 
although the theta of a put and a call with the same strike and expiration date are not 
equal to each other. 
Very long-term options are not subject to much time decay in one day's time. 
Thus, the theta of a long-term option is nearly zero. On the other hand, short-term 
options, especially at-the-money ones, have the largest absolute theta, since they are 
subject to the ravages of time on a daily basis. The theta of options on a highly volatile 
stock will be higher than the theta of options on a low-volatility stock. Obviously, the 
former options are more expensive (have more time value) and therefore have more 
time value to lose on a daily basis, thereby implying that they have a higher theta. 
Finally, the decay is not linear - an option will lose a greater percent of its daily value 
near the end of its life. 
Figure 40-7 (see Table 40-7) depicts the relationships of thetas for various strik­
ing prices and for differing volatilities on options with three months of life remain­
ing. Again, notice that for very volatile stocks, the out-of-the-money options have 
thetas as large as the at-the-moneys. This is saying that as each day passes, the prob­
ability of the stock reaching that out-of-the-money strike drops and causes the option