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 c_{0} + (X – FT) / (1+R)^{T} = p_{0}. Since X = FT for an at-the-money option, the put and the call have the same value for an at-the-money option.