644 Part V: Index Options and Futures 
These same strategies apply to options on futures. However, boxes on cash­
based options involve another consideration. It is often the case with cash-based 
options that the box sells for more than the difference in the strikes. For example, a 
box in which the strikes are 10 points apart might sell for 10.50, a substantial premi­
um over the striking price differential. The reason that this happens is because of the 
possibility of early assignment. The seller of the box assumes that risk and, as a result, 
demands a higher price for the box. 
If he sells the box for half a point more than the striking price differential, then 
he has a built-in cushion of .50 point of index movement if he were to be assigned 
early. In general, box strategies are not particularly attractive. However, if the pre­
mium being paid for the box is excessively high, then one should consider selling the 
box. Since there are four commissions involved, this is not normally a retail strategy. 
MATHEMATICAL APPLICATIONS 
The following material is intended to be a companion to Chapter 28 on mathemati­
cal applications. Index options have a few unique properties that must be taken into 
account when trying to predict their value via a model. 
The Black-Scholes model is still the model of choice for options, even for index 
options. Other models have been designed, but the Black-Scholes model seems to 
give accurate results without the extreme complications of most of the other models. 
FUTURES 
Modeling the fair value of most futures contracts is a difficult task. The 
Black-Scholes model is not usable for that task. Recall that we saw earlier that the 
fair value of a future contract on an index could be calculated by computing the pres­
ent value of the dividend and also knowing the savings in carrying cost of the futures 
contract versus buying the actual stocks in the index. 
CASH-BASED INDEX OPTIONS 
The futures fair value model for a capitalization-weighted index requires knowing the 
exact dividend, dividend payment date, and capitalization of each stock in the index 
(for price-weighted indices, the capitalization is unnecessary). This is the only way of 
getting the accurate dividend for use in the model. The same dividend calculation 
must be done for any other index before the Black-Scholes formula can be applied. 
In the actual model, the dividend for cash-based index options is used in much 
the same way that dividends are used for stock options: The present value of the div-