876 Part VI: Measuring and Trading Volatility 
is quantified by using theta. Furthermore, it serves to show that this position, which 
is delta neutral, is not neutral with respect to the passage of time. 
Finally, let us examine the position with respect to changes in volatility. This is 
done by calculating the position vega. 
XYZ:88 
Position 
Sold 1 00 July 90 calls 
Sold 100 July 90 puts 
Option 
Vega 
0.18 
0.18 
Position 
Vega 
-$1,800 
-$1,800 
-$3,600 
Again, this information is displayed at the time the position was established, 
three months to expiration, and with a volatility of 30% for XYZ. The vega is quite 
large. The fact that the call's vega is 0.18 means that the call price is expected to 
increase by 18 cents if the implied volatility of the option increases by one percent­
age point, from 30% to 31 %. Since the position is short 100 calls, an increase of 18 
cents in the price of the call would translate into a loss of $1,800. The put has a sim­
ilar vega, so the overall position would lose $3,600 if the options trade with an 
increase in volatility of just one percentage point. Of course, the position would make 
$3,600 if the volatility decreased by one percentage point, to 29%. 
This volatility risk, then, is the greatest risk in this short straddle position. As 
before, it is obvious that an increase in volatility is not good for a position with naked 
options in it. The use of vega quantifies this risk and shows how important it is to 
attempt to sell overpriced options when establishing such positions. One should not 
adhere to any one strategy all the time. For example, one should not always be sell­
ing naked puts. If the implied volatilities of these puts are below historical norms, 
such a strategy is much more likely to encounter the risk represented by the posi­
tion vega. There have been several times in the recent past - mostly during market 
crashes - when the implied volatilities of both index and equity options have leaped 
tremendously. Those times were not kind to sellers of options. However, in almost 
every case, the implied volatility of index options was quite low before the crash 
occurred. Thus, any trader who was examining his vega risk would not have been 
inclined to sell naked options when they were historically "cheap." 
In summary then, this "neutral" position is, in reality, much more complex when 
one considers all the other factors.