752 Part VI: Measuring and Trading Volatility 
The above example assumed that the stock was making instantaneous changes 
in price. In reality, of course, time would be passing as well, and that affects the vega 
too. Table 37-2 shows how the vega changes when time changes, all other factors 
being equal. 
Example: In this example, the following items are held fixed: stock price (50), strike 
price (50), implied volatility (70%), risk-free interest rate (5%), and dividend\(0). But 
now, we let time fluctuate. 
Table 37-2 clearly shows that the passage of time results not only in a decreas­
ing call price, but in a decreasing vega as well. This makes sense, of course, since one 
cannot expect an increase in implied volatility to have much of an effect on a very 
short-term option - certainly not to the extent that it would affect a LEAPS option. 
Some readers might be wondering how changes in implied volatility itself would 
affect the vega. This might be called the "vega of the vega," although I've never actu­
ally heard it referred to in that manner. The next table explores that concept. 
Example: Again, some factors will be kept constant - the stock price (50), the time 
to July expiration (3 months), the risk-free interest rate (5%), and the dividend (0). 
Table 37-3 allows implied volatility to fluctuate and shows what the theoretical price 
of a July 50 call would be, as well as its vega, at those volatilities. 
Thus, Table 37-3 shows that vega is surprisingly constant over a wide range of 
implied volatilities. That's the real reason why no one bothers with "vega of the vega." 
Vega begins to decline only if implied volatility gets exceedingly high, and implied 
volatilities of that magnitude are relatively rare. 
One can also compute the distance a stock would need to rise in order to over­
come a decrease in volatility. Consider Figure 37-1, which shows the theoretical price 
TABLE 37-2 
Implied Time Theoretical 
Stock Price Volatility Remaining Call Price Vega 
50 70% One year 14.60 0.182 
Six months 10.32 0.135 
Three months 7.25 0.098 
Two months 5.87 0.080 
One month 4.16 0.058 
Two weeks 2.87 0.039 
One week 1.96 0.028 
One day 0.73 0.010