Put/Call parity on fx

[nodes]

I missed this one:
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 matures at X at option expiration.
B) A put option on the forward at exercise price (X).
C) A put option, long the underlying asset, and short a risk-free bond that pays X-FT at option expiration.
D) Long the forward contract, short the put, and long a risk-free bond that pays X at option expiration.

 

[waqas43]

Opinion:
It is B. Don’t get confused by put call parity here. At the initiation of the contract, both call and put options are priced to have a value zero (mostly). At the money covers this mostly thing.
Someonee please correct me.

 

[kabhii]

Not sure but is it A?

 

[waqas43]

If you base your answer on Put / Call Parity, it is A indeed, cause thats the correct equation.

 

[sumimasin]

shouldnt we use the forward put call parity to answr this??

 

[AllLevelsPass]

My answer is A

 

[jlpalu]

I don’t agree. It’s the ARBITRAGE that should have a zero value (i.e. the PUT-CALL parity should hold at initiation), while both call and put options do have a price at initiation…
So to me is: C).

 

[nodes]

waqas43 was right:
Your answer: C was incorrect. The correct answer was B) 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.

 

[jlpalu]

i think you’re right… You DO NOT have the underlying asset (S) because its cost is zero (you do not have to pay for a future today).
OK, it’s B.
Thanks, nodes!