But the change makes sense intuitively, too, when a call is considered as a
cheaper substitute for owning the stock. For example, compare a $100 stock
with a three-month 60-strike call on that same stock. Being so far ITM,
there would likely be no time value in the call. If the call can be purchased
at parity, which alternative would be a superior investment, the call for $40
or the stock for $100? Certainly, the call would be. It costs less than half as
much as the stock but has the same reward potential; and the $60 not spent
on the stock can be invested in an interest-bearing account. This interest
advantage adds value to the call. Raising the interest rate increases this
value, and lowering it decreases the interest component of the value of the
call.
A similar concept holds for puts. Professional traders often get a short-
stock rebate on proceeds from a short-stock sale. This is simply interest
earned on the capital received when the stock is shorted. Is it better to pay
interest on the price of a put for a position that gives short exposure or to
receive interest on the credit from shorting the stock? There is an interest
disadvantage to owning the put. Therefore, a rise in interest rates devalues
puts.
This interest effect becomes evident when comparing ATM call and put
prices. For example, with interest at 5 percent, three-month options on an
$80 stock that pays a $0.25 dividend before option expiration might look
something like this:
The ATM call is higher in theoretical value than the ATM put by $0.75.
That amount can be justified using put-call parity:
(Here, simple interest of $1 is calculated as 80 × 0.05 × [90 / 360] = 1.)
Changes in market conditions are kept in line by the put-call parity. For
example, if the price of the call rises because of an increase in IV, the price
of the put will rise in step. If the interest rate rises by a quarter of a
percentage point, from 5 percent to 5.25 percent, the interest calculated for
three months on the 80-strike will increase from $1 to $1.05, causing the