37 lines
1.9 KiB
Plaintext
37 lines
1.9 KiB
Plaintext
Appendix C: Put-Call Parity • 289
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traded on the New Y ork Stock Exchange and the price of IBM traded in
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Philadelphia) but are not. An arbitrageur, once he or she spots the small
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difference, sells the more expensive thing and buys the less expensive one
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and makes a profit without accepting any risk.
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Because we are going to investigate dividend arbitrage, even a big-
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picture guy like me has to get down in the weeds because the differences we
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are going to try to spot are small ones. The weeds into which we are wading
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are mathematical ones, I’m afraid, but never fear—we’ll use nothing more
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than a little algebra. We’ll use these variables in our discussion:
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K = strike price
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C
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K = call option struck at K
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PK = put option struck at K
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Int = interest on a risk-free instrument
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Div = dividend payment
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S = stock price
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Because we are talking about arbitrage, it makes sense that we are
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going to look at two things, the value of which should be the same. We
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are going to take a detailed look at the preceding image, which means that
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we are going to compare a position composed of options with a position
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composed of stock.
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Let’s say that the stock at which we were looking to build a position is
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trading at $50 per share and that options on this stock expire in exactly one
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year. Further, let’s say that this stock is expected to yield $0.25 in dividends
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and that the company will pay these dividends the same day that the op-
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tions expire.
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Let’s compare the two positions in the same way as we did in the
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preceding big-picture image. As we saw in that image, a long call and a
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short put are the same as a stock. Mathematically, we would express this
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as follows:
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C
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K − PK = SK
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Although this is simple and we agreed that it’s about right, it is not
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technically so.
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The preceding equation is not technically right because we know that
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a stock is an unlevered instrument and that options are levered ones. In the |