32 lines
2.2 KiB
Plaintext
32 lines
2.2 KiB
Plaintext
Why the Numbers Don’t Don’t Always
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Add Up
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There will be many times when studying the rho of options in an option
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chain will reveal seemingly counterintuitive results. To be sure, the numbers
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don’t always add up to what appears logical. One reason for this is
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rounding. Another is that traders are more likely to use simple interest in
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calculating value, whereas the model uses compound interest. Hard-to-
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borrow stocks and stocks involved in mergers and acquisitions may have
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put-call parities that don’t work out right. But another, more common and
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more significant fly in the ointment is early exercise.
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Since the interest input in put-call parity is a function of the strike price, it
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is reasonable to expect that the higher the strike price, the greater the effect
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of interest on option prices will be. For European options, this is true to a
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large extent, in terms of aggregate impact of interest on the call and put pair.
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Strikes below the price where the stock is trading have a higher rho
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associated with the call relative to the put, whereas strikes above the stock
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price have a higher rho associated with the put relative to the call.
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Essentially, the more in-the-money an option is, the higher its rho. But with
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European options, observing the aggregate of the absolute values of the call
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and put rhos would show a higher combined rho the higher the strike.
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With American options, the put can be exercised early. A trader will
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exercise a put before expiration if the alternative—being short stock and
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receiving a short stock rebate—is a wiser choice based on the price of the
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put. Professional traders may own stock as a hedge against a put. They may
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exercise deep ITM puts (1.00-delta puts) to avoid paying interest on capital
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charges related to the stock. The potential for early exercise is factored into
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models that price American options. Here, when puts get deeper in-the-
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money—that is, more apt to be exercised—the rho decreases. When the
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strike price is very high relative to the stock price—meaning the put is very
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deep ITM—and there is little or no time value left to the call or the put, the
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aggregate put-call rho can be zero. Rho is discussed in greater detail in
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Chapter 7. |