Chapter 39: Volatility Trading Techniques 825 
Speaking of neutrality, one can also use the deltas of the options in question to 
alter the ratio of puts to calls, making the position initially as neutral as possible. This 
is the suggested approach, since the volatility buyer does not care whether the stock 
goes up or down. He is merely interested in stock movement and/or an increase in 
implied volatility. 
Example: XYZ is again trading at 39.60, and the trader wants a neutral position. He 
should use the deltas of the options to construct a neutral position. Consider the 
October 40 straddle, for example. Assume the volatility used for the probability cal­
culations is 40%. Under those conditions (and the ones assumed in the previous 
example), the October 40 call has a delta of 0.60 and the October 40 put has a delta 
of -0.40. Thus a ratio of buying 2 calls and 3 puts is a neutral ratio. If the call is sell­
ing for 6 and the put is selling for 5, then the break-even points for a 2-by-3 position 
would be 53.5 on the upside and 31 on the downside. This information is summarized 
as follows: 
Delta of October 40 call: 
Delta of October 40 put: 
+0.60 
-0.40 
Delta-neutral ratio: buy 2 calls and 3 puts 
Price of October 40 coll: 
Price of October 40 put: 
Net cost of 2-by-3 position: 27 points 
Break-even points: 
6.00 
5.00 
Upside = 40 + 27 /2 = 53.50 
Downside = 40 - 27 /3 = 31 .00 
So, the probability calculations would endeavor to determine what the chances are of 
the stock ever trading at either 53.50 or 31.00 at any time prior to expiration. In fact, 
since there are straddles available in several expiration months, the strategist would 
want to analyze each of them in a similar fashion. Table 39-1 shows how his choices 
might look. If one were considering buying a strangle, similar calculations could be 
made using the deltas of the put and the call, where the call strike is higher than the 
put strike. 
Another simple strategy that can be used when volatility is low is the calendar 
spread, because it has a positive vega. That is, it can be expected to expand if implied 
volatility increases. For most traders, though, the limited profit nature of the calen-