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+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