Cl,apter 34: Futures and Futures Options 669 
Now let us consider an option example. In this type of calculation, the exchange 
uses the same moves by the underlying futures contract and calculates the option 
theoretical values as they would exist on the next trading day. One calculation is per­
formed for volatility increasing and one for volatility decreasing. 
Example: Using the same S&P 500 futures contract, the following array might depict 
the risk array for a long December 410 call. One does not need to know the option 
or futures price in order to use the array; the exchange incorporates that information 
into the model used to generate the potential gains and losses. 
Scenario 
Futures unchanged; volatility up 
Futures unchanged; volatility down 
Futures up one-third of range; volatility up 
Futures up one-third of range; volatility down 
Futures down one-third of range; volatility up 
Futures down one-third of range; volatility down 
Futures up two-thirds of range; volatility up 
Futures up two-thirds of range; volatility down 
Futures down two-thirds of range; volatility ur 
Futures down two-thirds of range; volatility /o:n 
Futures up three-thirds of range; volatility up 
Futures up three-thirds of range; volatility down 
Futures down three-thirds of range; volatility up 
Futures down three-thirds of range; volatility down 
Futures up "extreme" move 
Futures down "extreme" move 
Long 1 
Dec 410 call 
Potential 
Ph/Loss 
+ 460 
610 
+ 2,640 
+ 1,730 
- 1,270 
- 2,340 
+ 5,210 
+ 4,540 
- 2,540 
- 3,430 
+ 8,060 
+ 7,640 
- 3,380 
- 3,990 
+ 3,130 
- 1,500 
The items in the risk array are all quite logical: Upward futures movements pro­
duce profits and downward futures movements produce losses in the long call posi­
tion. Moreover, worse results are always obtained by using the lower volatility as 
opposed to the higher one. In this particular example, the SPAN requirement would 
be $3,990 ("futures down three-thirds; volatility down"). That is, the SPAN system 
predicts that you could lose $3,990 of your call value if futures fell by their entire 
range and volatility decreased - a worst-case scenario. Therefore, that is the amount 
of margin one is required to keep for this long option position.