Question

Now consider European options on AAPL with Expirations other than 6 months.
Suppose there also exists a forward contract on AAPL with 12-month forward price =
F12. Again, ignore AAPL’s dividend.
a)
First consider 12-month European options on AAPL. What can we say about the
relative value of a European put on AAPL with K = F12, and a European call on
AAPL with K = F12?

b)
What can you say about the relative values of a European calls and puts on AAPL
if they are struck at some K > F12?

c)
What can you say about the relative prices of T-month European puts and calls if
both options have K = FT?

Answer 1

a) The given situation refers to a case of Put-Call Parity which is a relationship of European Put and Call Option,with identical Strike Price and Expiry.

So the portfolio will have a long call option and Short put option which gets similar to a single forward contract at this Strike Price and Expiry. The call will be exercised if the price at expiry is above the strike price and Put will be exercise if at expiry the price is lower than Strike Price.

The investor would be paying the net premimum which is (Premium earned on short put option - Premimum paid on doing long call option)

b In the second case, when the Strike Price is expected to be higher than the Future Price...the investor would do a fence strategy wherein he will sell call option and buy put options. using out of the money strike price levels

This would help in setting the maximum downside(Put Option) and reduce premium expense with limited upside profit potential (call option)

c) The third situation would have a similar treatment as the first one. Its a case of Put-Call Parity which is a relationship of European Put and Call Option,with identical Strike Price and Expiry.

So the portfolio will have a long call option and Short put option which gets similar to a single forward contract at this Strike Price and Expiry.

However the premium would differ based on the month of expiry. The longer the expiry the less the premium and vice versa.