Chapter 39: Volatility Trading Techniques 829 
TABLE 39-2 
September September September September 
800 call 750 call 730 call 700 call 
September September September September 
Naked sale: 500 put 550 put 570 put 600 put 
Call price 0.20 1.50 3.50 8.80 
Put price 0.40 2.00 3.70 8.50 
Probability of call strike 4% 17% 30% 44% 
Probability of put strike 1% 11% 20% 40% 
vide much of a return even if they expire worthless. Remember that one is 
required to establish the position with margin of at least 10% of the index price 
for naked index options, which would be $6,500 in this case. In fact, it has been 
recommended that one margin the position at the striking price itself (15% of 800, 
or $12,000 in this case). So, taking in only $60, less commissions, for the sale of 
the September 500-800 strangle doesn't seem to provide enough of a reward. 
Thus, the best choice seems to be the September 550-750 strangle. One would be 
making about $320 after commissions if the options expired worthless, and the 
recommended margin would be 15% of 750 (the higher strike), or $11,250 - a 
return of about 2.8% for one month. One cannot annualize these returns, for he 
has no idea if the same option pricing structure will exist in five weeks, when these 
options expire. 
Other probabilities can be calculated as well. For example, suppose one has 
decided to buy a straddle. He might want to know what the odds are not only of 
breaking even, but also of making at least a certain percentage return- say 20%. One 
could also calculate the probability of the stock moving 20% past the break-even 
points. That distance - 20% - is a reasonable figure to use because one would most 
likely be taking some partial profits or adjusting his position if the stock did indeed 
move that far. 
USING STOCK PRICE HISTORY 
All of the work done so far - determining which options are expensive, selecting a 
strategy, and calculating the probabilities of success - has been somewhat theoretical 
in that we haven't done any "back testing" with regard to the volatility of the under­
lying instruments. At this point, one should look at past prices to see if the stock has 
been able to make large moves (whether or not such a move is desired).