put-call parity

[sheridan]

What does the put-call parity tell me? I'm studying from Broverman's study manual.

[Gandalf]

It gives you a relationship between the price of a call and the price of a put, assuming both are for the same strike price on the same date.

[Bama Gambler]

A synthetic forward can be created by buying a call at strike K and selling a put at strike K. The cost of this forward is Call(K,T) - Put(K,T). A true forward has a premium of 0. So if Call(K,T) - Put(K,T) > 0, then your right to buy at price K must be smaller than the forward price (call it F), otherwise you would just enter into a forward (which has no upfront cost) instead of buying a call and selling a put. Put-call parity says the present value of this discount must be equal to the cost of the synthetic forward:
PV(discount) = cost to create synthetic forward
PV(F-K) = Call(K,T) - Put(K,T)

[krzysio]

Originally Posted by Bama Gambler

A synthetic forward can be created by buying a call at strike K and selling a put at strike K. The cost of this forward is Call(K,T) - Put(K,T). A true forward has a premium of 0. So if Call(K,T) - Put(K,T) > 0, then your right to buy at price K must be smaller than the forward price (call it F), otherwise you would just enter into a forward (which has no upfront cost) instead of buying a call and selling a put. Put-call parity says the present value of this discount must be equal to the cost of the synthetic forward:
PV(discount) = cost to create synthetic forward
PV(F-K) = Call(K,T) - Put(K,T)

And since price is a linear operator and PV(F) is the spot price, you can also say it as
S - PV(K) = Call - Put
which for me is the easiest way to remember. It also can be stated nicely this way:
Call = S - PV(K) + Put
which shows that paying employees in options amounts to massive exploitation of Capitalists by employees, especially executives.

Yours,
Krzys'