860 Part VI: Measuring and Trading Volatility 
Example: Again, assume XYZ is at 49, and the January 50 call is selling for 3.50. The 
vega of the option is 0.25, and the current volatility of XYZ is 30%. 
If the volatility increases by one percentage point or 1 % to 31 %, then the vega 
indicates that the option will increase in value by 0.25, to 3. 75. 
If the volatility had instead decreased by 1 percent to 29%, then the January 50 
call would have decreased to 3.25 (a loss of 0.25, the amount of the vega). 
If the implied volatility of an option increases, the option price will increase as 
well. Consequently, even though XYZ stock may be exhibiting the same historic 
movement that it always has, and therefore its (historical) volatility would be 
unchanged, if option buyers appear in sufficient quantity, they may drive the implied 
volatility of XYZ's options higher. Likewise, an excess of option sellers could drive the 
implied volatility lower, even though the historical volatility does not change. So, it 
must be concluded that vega measures how much the option price changes as implied 
volatility changes. 
Vega is related to time. Figure 40-6 (see Table 40-6) shows the vegas for options 
with differing times remaining until expiration. The underlying stock is assumed to 
be 50 in all cases. Notice that the more time that remains, the higher the vega is. It 
is interesting to note that, for very long-term options, the vega of the slightly out-of­
the-money calls (strike = 55) is actually higher than that of the at-the-money. 
However, this discrepancy disappears as time passes. Not shown, but equally true, is 
that the vega of a slightly out-of-the-money option on a very volatile stock may be 
higher than that of the at-the-money. 
As with the measurements of risk discussed already, vega can refer to the option 
itself ("option vega") or to the position as a whole ("position vega"). Since vega is 
expressed as a positive number, if one is long options, then his position vega will be 
positive. This means he has exposure if volatilities decrease, or can make money if 
volatilities increase. 
Example: Again, assume that we have the same backspread position as before, with 
XYZ at 31.75. 
Option Position 
Position Vega Vego 
Short 4,500 XYZ 0.00 0 
Short 100 XYZ April 25 calls 0.02 - 200 
Long 50 XYZ April 30 calls 0.05 + 250 
Long 139 XYZ July 30 calls 0.07 + 973 
Total Vega: + 1,023