37 lines
2.8 KiB
Plaintext
37 lines
2.8 KiB
Plaintext
Chapter 33: Mathematical Considerations for Index Products 643
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For index futures options, there is no risk when the underlying closes near the
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strike, since they settle for cash. One is not forced to make a choice as to whether to
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exercise his calls. (See Chapter 27 on arbitrage for a description of risks at expiration
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when trading reversals or conversions.)
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In actual practice, floor traders may attempt to establish conversions in futures
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options for small increments - perhaps 5 or 10 cents in S&P futures, for example.
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The arbitrageur should note that futures options do actually create a credit or debit
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in the account. That is, they are like stock options in that respect, even though the
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underlying instrument is not. This means that if one is using a deep in-the-money
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option in the conversion, there will actually be some carrying cost involved.
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Example: An index future is trading at 179.00 and one is going to price the
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December 190 conversion, assuming that December expiration is 50 days away.
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Assume that the current carrying cost of money is 10% annually. Finally, assume that
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the December 190 call is selling for 1.00, and the December 190 put is selling for
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11.85. Note that the put has a time value premium of only 85 cents, less than the pre
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mium of the call. The reason for this is that one would have to pay a carrying cost to
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do the December 190 conversion.
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If one established the 190 conversion, he would buy the futures (no credit or
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debit to the account), buy the put (a debit of 11.85), and sell the call (a credit of 1.00).
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Thus, the account actually incurs a debit of 10.85 from the options. The carrying cost
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for 10.85 at 10% for 50 days is 10.85 x 10% x 50/365 = 0.15. This indicates that the
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converter is willing to pay 15 cents less time premium for the put (or conversely that
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the reversal trader is willing to sell the put for 15 cents less time premium). Instead
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of the put trading with a time value premium equal to the call price, the put will trade
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with a premium of 15 cents less. Thus, the time premium of the put is 85 cents,
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rather than being equal to the price of the call, 1.00.
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BOX SPREADS
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Recall that a "box" consists of a bullish vertical spread involving two striking prices,
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and a bearish vertical spread using the same two strikes. One spread is constructed
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with puts and the other with calls. The profitability of the box is the same regardless
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of the price of the underlying security at expiration.
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Box arbitrage with equity options involves trying to buy the box for less than the
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difference in the striking prices, for ~ple, trying to buy a box in which the strikes
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are 5 points apart for 4. 75. Selling the box for more than 5 points would represent
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arbitrage as well. In fact, even selling the box at exactly 5 points would produce a
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profit for the arbitrageur, since he earns interest on the credit from the sale. |