# future and forward put call parity

Dear All:

Why is that X=FT for an at the money option? as the problem below.

thank you so much for your time.

Which of the following would have the same value at t = 0 as an at-the-money call option on a forward contract priced at FT (the forward price at time = 0)?

A) A put option, long the underlying asset, and short a risk-free bond that pays X-FT at option expiration. B) A put option, long the underlying asset, and short a risk-free bond that matures at X at option expiration. C) A put option on the forward at exercise price (X).

Your answer: B was incorrect. The correct answer was C) A put option on the forward at exercise price (X).

Put-call parity for options on forward contracts is c0 + (X – FT) / (1+R)T = p0. Since X = FT for an at-the-money option, the put and the call have the same value for an at-the-money option.

Co+X/(1+r)^T = P + S0

If the forward were properly priced S0 * (1+r)^T = Ft

so S0 = Ft/(1+r)^T

and you get the above…