We know that $$C-P = PV(F_{0,T}-K)$$

When we create a synthetic forward, we buy call and sell a put at the same strike price $K$. When we buy the call why do we assume the premium is positive? When we sell the put, why do we assume the premium is negative?

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You can accept one of the answers if you are satisfied by it :-) –  vonjd Jan 28 '13 at 16:15

Both premiums are actually always positive by definition. The difference will be positive when the forward price exceeds the strike and vice versa.

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