37 lines
2.1 KiB
Plaintext
37 lines
2.1 KiB
Plaintext
Appendix C: Put-Call Parity • 291
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acts as a “negative drift” term in the BSM. When a dividend is paid, theory
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says that the stock price should drop by the amount of the dividend. Be-
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cause a drop in price is bad for the holder of a call option, the price of a call
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option is cheaper by the amount of the expected dividend.
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Thus, for a dividend-paying stock, to establish an option-based position
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that has exactly the same characteristics as a stock portfolio, we have to keep
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the expected amount of the dividend in our margin account.
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1 This money
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placed into the option position will make up for the dividend that will be
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paid to the stock holder. Here is how this would look in our equation:
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C
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K − PK + (K − Int) + Div = S
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With the dividend payment included, our equation is complete.
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Now it is time for some algebra. Let’s rearrange the preceding equa-
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tion to see what the call option should be worth:
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CK = PK + Int − Div + (S − K)
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Taking a look at this, do you notice last term (S – K )? A stock’s price
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minus the strike price of a call is the intrinsic value. And we know that
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the value of a call option consists of intrinsic value and time value. This
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means that
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/dncurlybracketleft/dncurlybracketmid/horizcurlybracketext/horizcurlybracketext/dncurlybracketright/horizcurlybracketext/horizcurlybracketext/dncurlybracketleft/dncurlybracketmid/dncurlybracketright=+ −−CP SKKK IntD iv + ()
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Time valueI ntrinsic value
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So now let’s say that time passes and at the end of the year, the stock
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is trading at $70—deep ITM for our $50-strike call option. On the day
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before expiration, the time value will be very close to zero as long as the op-
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tion is deep ITM. Building on the preceding equation, we can put the rule
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about the time value of a deep ITM option in the following mathematical
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equation:
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P
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K + Int − Div ≈ 0
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If the time value ever falls below 0, the value of the call would trade for less
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than the intrinsic value. Of course, no one would want to hold an option
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that has negative time value. In mathematical terms, that scenario would
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look like this:
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P
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K + Int − Div < 0 |