Quote from aradiel:
So if the carry cost is not zero, the market will not give the same extrinsic value to calls and puts, right?
No, if carry is not zero then the call's extrinsic value will be greater by the amount of carry. If you adjust for carry then it will be the same.
So this is not a mispricing nor it is an arb, this is put-call parity.
That is, if you were to sell the call, buy the put and the stock to lock in the "extra" extrinsic value in the call then you would pay the carry on the long stock and thus your profit will be zero.

