720 Part V: Index Options and Futures 
where vi = volatility 
Pi = price of the underlying 
ui = unit of trading of the option 
Lli = delta of the option 
Example: Suppose that one indeed wants to buy crude oil calls and also buy puts on 
the XOI Index because he thinks that crude oil is cheap with respect to oil stocks. 
The following prices exist: 
July crude futures: 16.35 
Crude July 1550 call: 1.10 
Volatility: 25% 
Call delta: O. 7 4 
$XOI: 256.50 
June 265 put: 14½ 
Volatility: 17% 
Put delta: 0. 73 
The unit of trading for XOI options is $100 per point, as it is with nearly all stock and 
index options. The unit of trading for crude oil futures and options is $1,000 per 
point. With all of this information, the ratio can be computed: 
Crude= 1,000 x 0.25 x 16.35 x 0.74 
XOI = 100 x 0.17 x 256.50 x 0.73 
Ratio = Crude/ XOI = 0.91 
Therefore, one would buy 0.91 XOI put for every 1 crude oil call that he bought. For 
small accounts, this is essentially a 1-to-l ratio, but for large accounts, the exact ratio 
could be used (for example, buy 91 XOI puts and 100 crude oil calls). The resultant 
quantities encompass the various differences in these two markets - mainly the price 
and volatility of the underlyings, plus the large differential in their units of trading 
(100 vs. 1,000). 
SUMMARY 
Futures spreading is a very important and potentially profitable endeavor. Utilizing 
options in these spreads can often improve profitability to the point that an originally 
mistaken assumption can be overcome by volatility of price movement.