Chapter 33: Mathematical Considerations for Index Products 643 
For index futures options, there is no risk when the underlying closes near the 
strike, since they settle for cash. One is not forced to make a choice as to whether to 
exercise his calls. (See Chapter 27 on arbitrage for a description of risks at expiration 
when trading reversals or conversions.) 
In actual practice, floor traders may attempt to establish conversions in futures 
options for small increments - perhaps 5 or 10 cents in S&P futures, for example. 
The arbitrageur should note that futures options do actually create a credit or debit 
in the account. That is, they are like stock options in that respect, even though the 
underlying instrument is not. This means that if one is using a deep in-the-money 
option in the conversion, there will actually be some carrying cost involved. 
Example: An index future is trading at 179.00 and one is going to price the 
December 190 conversion, assuming that December expiration is 50 days away. 
Assume that the current carrying cost of money is 10% annually. Finally, assume that 
the December 190 call is selling for 1.00, and the December 190 put is selling for 
11.85. Note that the put has a time value premium of only 85 cents, less than the pre­
mium of the call. The reason for this is that one would have to pay a carrying cost to 
do the December 190 conversion. 
If one established the 190 conversion, he would buy the futures (no credit or 
debit to the account), buy the put (a debit of 11.85), and sell the call (a credit of 1.00). 
Thus, the account actually incurs a debit of 10.85 from the options. The carrying cost 
for 10.85 at 10% for 50 days is 10.85 x 10% x 50/365 = 0.15. This indicates that the 
converter is willing to pay 15 cents less time premium for the put (or conversely that 
the reversal trader is willing to sell the put for 15 cents less time premium). Instead 
of the put trading with a time value premium equal to the call price, the put will trade 
with a premium of 15 cents less. Thus, the time premium of the put is 85 cents, 
rather than being equal to the price of the call, 1.00. 
BOX SPREADS 
Recall that a "box" consists of a bullish vertical spread involving two striking prices, 
and a bearish vertical spread using the same two strikes. One spread is constructed 
with puts and the other with calls. The profitability of the box is the same regardless 
of the price of the underlying security at expiration. 
Box arbitrage with equity options involves trying to buy the box for less than the 
difference in the striking prices, for ~ple, trying to buy a box in which the strikes 
are 5 points apart for 4. 75. Selling the box for more than 5 points would represent 
arbitrage as well. In fact, even selling the box at exactly 5 points would produce a 
profit for the arbitrageur, since he earns interest on the credit from the sale.