Chapter 33: Mathematical Considerations for Index Products 64S 
idend is subtracted from the index price and the model is evaluated using that adjust­
ed stock price. With stock options, there was a second alternative - shortening the 
time to expiration to be equal to the ex-date - but that is not viable with index options 
since there are numerous ex-dates. 
Let's look at an example using the same fictional dividend information and index 
that were used in Chapter 30 on stock index hedging strategies. 
Example: Assume that we have a capitalization-weighted index composed of three 
stocks: AAA, BBB, and CCC. The following table gives the pertinent information 
regarding the dividends and floats of these three stocks: 
Dividend Days until 
Stock Amount Dividend Float 
AAA 1.00 35 50,000,000 
BBB 0.25 60 35,000,000 
CCC 0.60 8 120,000,000 
Divisor: 150,000,000 
One first computes the present worth of each stock's dividend, multiplies that 
amount by the float, and then divides by the index divisor. The sum of these compu­
tations for each stock gives the total dividend for the index. The present worth of the 
dividend for this index is $0.8667. 
Assume that the index is currently trading at 175.63 and that we want to evalu­
ate the theoretical value of the July 175 call. Then, using the Black-Scholes model, 
we would perform the following calculations: 
1. Subtract the present worth of the dividend, 0.8667, from the current index price 
of 175.63, giving an adjusted index price of 174.7633. 
2. Evaluate the call's fair value using 17 4. 7633 as the stock price. All other variables 
are as they are for stocks, including the risk-free interest rate at its actual value 
(10%, for example). 
The theoretical value for puts is computed in the same way as for equity 
options, by using the arbitrage model. This is sufficient for cash-based index options 
because it is possible - albeit difficult to hedge these options by buying or selling 
the entire index. Thus, the options should reflect the potential for such arbitrage. 
The put value should, of course, reflect the potential for dividend arbitrage with the 
index. The arbitrage valuation model p"resented in Chapter 28 on modeling called for 
the dividend to be used. For these index puts, one would use the present worth of