Show that european call, put with same maturity and strike are equal iff strike=forward price

[barrycohen]

The book defines put call parity as:
\( P(t)+S(t)-C(t) = Ke^{-r(T-t)} \)
where P(t) is value of the put, C(t) value of the call, S(t) is the value of the underlying asset, K is strike price.

In the proof, they substitute F (price of the forward) for the value of the asset. Why are they allowed to do this? Aren't the forward price and asset value different things?

Thanks!

 

[IntoDarkness]

why not? its just math substitution game

 

[barrycohen]

Update: Figured it out. Proof was using a different definition of put-call parity where asset pays dividends