Exercise 12.2.4 (1) Prove that a newly written forward contract is equivalent to a portfolio of one long European call and one short European put on the same underlying asset and expiration date with a common strike price equal to the forward price. (An option is said to be at the money forward if X= F.) (2) Prove the alternative put–call parity that says C = P for the call and put in (1). (3) Derive Lemma 12.2.1 from the put–call parity. (4) Verify that, by substituting the forward price in Eq. (12.3) for the strike price X in the Black–Scholes formula of Theorem 9.3.4, we obtain C = P.