Also, lets say interest rates are different than zero and positive, does it mean that a CC (OTM call) should result in premium since it has a bigger carry cost (or opportunity cost) than a NP (DIM put)? Maybe time value has more to do with the price of the underlying (and where the strike of the option stands) than with if the option is a call or a put.
They will be the same in terms of extrinsic value if they share a strike. There is something lost in the translation here.
I am using "time value" as the same as "extrinsic value". You are saying that calls and puts that share the same strike price should have the same extrinsic value. So, lets say XYZ is being traded at $ 30 and its june 33 calls are traded at 0.30. The june 33 put should be trading at 3.30, right? Also, can we verify this with real market quotes?
Adjusted for carry, yes. The difference between the call and put extrinsic value, if any, is related to dividends and carry.
Here's an option calculator. Put all the info in (zero interest and no div) and vary the volatility until it yields a call value of 30 cents. When that happens, the put will display $3.30 http://www.cboe.com/framed/IVolfram...ADING_TOOLS&title=CBOE - IVolatility Services Or would you prefer to keep asking the same question over and over again?
So if the carry cost is not zero, the market will not give the same extrinsic value to calls and puts, right?
You are right, I am making the same question in multiple ways to check the consistency of the responses that sometimes are comming different. Thanks for the link.