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

#### barrycohen

##### New Member

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

##### Well-Known Member
why not? its just math substitution game

#### barrycohen

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