586 Part V: Index Options and Futures 
the put and call are based on different underlying indices. This concept is discussed 
in more detail in Chapter 35 on futures spreads. 
The second way to use options in index spreading is to use options that are less 
deeply in-the-money. In such a case, one must use the deltas of the options in order 
to accurately compute the proper hedge. He would calculate the number of options 
to buy and sell by using the formula given previously for the ratio of the indices, 
which incorporates both price and volatility, and then multiplying by a factor to 
include delta. 
where 
vi is the volatility of index i 
Pi is the price of index i 
ui is the unit of trading 
and di is the delta of the selected option on index i 
Example: The following data is known: 
ZYX: 175.00, volatility= 20% 
UVX: 150.00, volatility = 15% 
ZYX Dec 175 put: 7, delta= - .45, worth $500/pt. 
UVX Dec 150 call: 5, delta= .52, worth $100/pt 
Suppose one decides that he wants to set up a position that will profit if the 
spread between the two cash indices shrinks. Rather than use the deeply in-the­
money options, he now decides to use the at-the-money options. He would use the 
option ratio formula to determine how many puts and calls to buy. (Ignore the put's 
negative delta for the purposes of this formula.) 
.20 175.00 500 .45 Option Ratio= -x ---x - x - = 6 731 .15 150.00 100 .52 . 
He would buy nearly 7 UVX calls for every ZYX put purchased. 
In the previous example, using in-the-money options, one had a very small 
expense for time value premium and could profit if the indices were volatile, even if 
the cash spread did not shrink. This position has a great deal of time value premium 
e:x--pense, but could make profits on smaller moves by the indices. Of course, either 
one could profit if the cash indices moved favorably.