This holds true whether the options are in-, at-, or out-of-the-money. For
example, with a stock at $54, the 50-put would have a −0.205 delta and the
call would have a 0.799 delta. Selling 100 shares against the call to create
the synthetic put yields a net delta of −0.201.
If long or short stock is added to a call or put to create a synthetic, delta
will be the only greek affected. With that in mind, note the other greeks
displayed in Exhibit 6.5 —especially theta. Proportionally, the biggest
difference in the table is in theta. The disparity is due in part to interest.
When the effects of the interest component outweigh the effects of the
dividend, the time value of the call can be higher than the time value of the
put. Because the call must lose more premium than the put by expiration,
the theta of the call must be higher than the theta of the put.
American exercise can also cause the option prices in put-call parity to
not add up. Deep in-the-money (ITM) puts can trade at parity while the
corresponding call still has time value. The put-call equation can be
unbalanced. The same applies to calls on dividend-paying stocks as the
dividend date approaches. When the date is imminent, calls can trade close
to parity while the puts still have time value. The role of dividends will be
discussed further in Chapter 8.