678 Part V: Index Options and Futures 
Example: The table below compares the theoretical values computed with the two 
formulae, where r = 6% and t = 0.25 (1/4 of a year). Furthermore, assume the futures 
price is 100. The strike price is given in the first column, and the put price is given 
in the second column. The predicted call prices according to each formula are then 
shown in the next two columns. 
Put Formula l Formula 2 
Strike Price (Simple) ( Using e-rf) 
70 0.25 30.25 29.80 
80 1.00 21.00 20.70 
90 3.25 13.25 13.10 
95 5.35 10.35 10.28 
100 7.50 7.50 7.50 
105 10.70 5.70 5.77 
110 13.90 3.90 4.05 
120 21.80 1.80 2.10 
For options that are 20 or 30 points in- or out-of-the-money, there is a notice­
able differential in these three-month options. However, for options closer to the 
strike, the differential is small. 
If the time remaining to expiration is shorter than that used in the example 
above, the differences are smaller; if the time is longer, the differences are magnified. 
Options on Physicals. Determining the fair value of options on physicals such 
as currencies is more complicated. The proper way to calculate the fair value of an 
option on a physical is quite similar to that used for stock options. Recall that in the 
case of stock options, one first subtracts the present worth of the dividend from the 
current stock price before calculating the option value. A similar process is used for 
determining the fair value of currency or any other options on physicals. In any of 
these cases, the underlying security bears interest continuously, instead of quarterly 
as stocks do. Therefore, all one needs to do is to subtract from the underlying price 
the amount of interest to be paid until option expiration and then add the amount of 
accrued interest to be paid. All other inputs into the Black-Scholes model would 
remain the same, including the risk-free interest rate being equal to the 90-day T-bill 
rate. 
Again, the practical option strategist has a shortcut available to him. If one 
assumes that the various factors necessary to price currencies have been assimilated 
into the futures markets in Chicago, then one can merely use the futures price as the 
price of the underlying for evaluating the physical delivery options in Philadelphia.