646 Part V: Index Options and Futures 
the dividend on the index - the same one that was used for the call valuation, as in 
the last example. 
THE IMPLIED DIVIDEND 
If one does not have access to all of the dividend information necessary to make the 
"present worth of the dividends" calculation (i.e., if he is a private individual or pub­
lic customer who does not subscribe to a computer-based dividend "service"), there 
is still a way to estimate the present worth of the dividend. All one need do is make 
the assumption that the market- makers know what the present worth of the dividend 
is, and are thus pricing the options accordingly. The individual public customer can 
use this information to deduce what the dividend is. 
Example: OEX is trading at 700, the June options have 30 days of life remaining, the 
short-term interest rate is 10%, and the following prices exist: 
June 700 call: 18.00 
June 700 put: 14.50 
One can use iterations of the Black-Scholes model to determine what the OEX 
"dividend" is. In this case, it turns out to be something on the order of $2.10. 
Briefly, these are the steps that one would need to follow in order to determine 
this dividend: 
1. Assume the dividend is $0.00. 
2. Using the assumed dividend, use the Black-Scholes model to determine the 
implied volatility of the call option, whose price is known (18.00 in the above 
example). 
3. Using the implied volatility determined from step 2 and the assumed dividend, 
is the arbitrage put value as derived from the Black-Scholes calculations at the 
end of step 2 roughly equal to the market value of the put (14.50 in the above 
example)? If yes, you are done. If not, increase the assumed dividend by some 
nominal amount, say $0.10, and return to step 2. 
Thus, without having access to complete dividend information, one can use the 
information provided to him by the marketplace in order to imply the dividend of an 
index option. The only assumption one makes is that the market-makers know what 
the dividend is (they most assuredly do). Note that the implied volatility of the 
options is determined concurrently with the implied dividend (step 2 above). A veiy 
useful tool, this simple "implied dividend calculator" can be added to any software 
that employs the Black-Scholes model.