Do synthetic relationships hold if call and put are at different strikes?

[Victor123]

Is there a way to extend the put call parity synthetic relationships to cover multiple strikes?

For example, I always hear that a covered call is a synthetic short put.
Does that statement only hold in this case:
Long stock at 100, sell 100 Call = short 100 Put

Or also in this case:
Long stock at 100, sell 105 call = short put ( which strike, 100 or 105)?

Is there a way to 'extrapolate' put call parity relationships to cover multiple expiry dates, when the call and the put are not having same expiry date?
My guess is no, but just want to confirm

 

[xandman]

yes.

105. Observe how close extrinsic value is. But mild differences always exist between the put and call skews.

No, because of the existence of a volatility curve across expirations.

 

[FSU]

It doesn't matter what price you buy the stock at, you will be synthetically short the put that is the same strike as the call you sold.