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