756 Part VI: Measuring and Trading Volatility 
Notice that the stock price is equal to the strike price (100). However, the deltas 
are not at all equal. In fact, the delta of the call is 1.5 times that of the put (in absolute 
value). One must buy three puts and two calls in order to have a delta-neutral posi­
tion. 
Most experienced option traders know that the delta of an at-the-money call is 
somewhat higher than that of an at-the-money put. Consequently, they often esti­
mate, without checking, that buying three puts and two calls produces a delta-neu­
tral "straddle buy." However, consider a similar situation, but with a much higher 
implied volatility- 110%, say. 
AAA Common: 100; Implied Volatility: 110% 
Option 
AAA October 100 call 
AAA October 1 00 put 
Price 
31.00 
28.00 
Delta 
0.67 
-0.33 
The delta-neutral ratio here is two-to-one (67 divided by 33), not three-to-two 
as in the earlier case - even though both stock prices are 100 and both sets of options 
have six months remaining. This is a big difference in the delta-neutral ratio, espe­
cially if one is trading a large quantity of options. This shows how different levels of 
implied volatility can alter one's perception of what is a neutral position. It also points 
out that one can't necessarily rely on his intuition; it is always best to check with a 
model. 
Carrying this thought a step further, one must be mindful of a change in implied 
volatility if he wants to keep his position delta-neutral. If the implied volatility of AAA 
options should drop significantly, the 2-to-l ratio will no longer be neutral, even if the 
stock is still trading at 100. Hence, a trader wishing to remain delta-neutral must 
monitor not only changes in stock price, but changes in implied volatility as well. For­
more complex strategies, one will also find the delta-neutral ratio changing due to a 
change in implied volatility. 
The preceding examples summarize the major variables that might affect the 
vega and also show how vega affects things other than itself, such as delta and, there­
fore, delta neutrality. By the way, the vega of the underlying is zero; an increase in 
implied volatility does not affect the price of the underlying instrument at all, in the­
ory. In reality, if options get very expensive (i.e., implied volatility spikes up), that 
usually brings traders into a stock and so the stock price will change. But that's not a 
mathematical relationship, just a market cause-and-effect relationship.