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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.