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