These are OH SO WRONG on so many levels! It boggles my mind that that there are people here that need to be convinced that put-call parity actually works, skew or no skew. So I propose this. jwcapital and nitro, what say you that we put some money on the table? Let's do some trades, you and I, and we'll establish who's right experimentally.
E.g., Log underlying = vanilla. Long Call, short Put at same strike = synthetic equivalent of above. I am not sure what you don't understand.
Yes. It is very possible that the synthetic equivalent can outperform the natural version. This happened in the SPX index options pit when we were at 775 ish or so when the market was in free fall. The synthetic puts were way better trade than the outright put. In fact, I am talking empirically, not theoretically.
Cool, sounds good... I would assume you prefer stocks or indices as underlying? If so, tell me what underlying you like (I am not an equities person) and we can proceed.
ES or SPX options. For example, make me a market on any short dated ATM or OTM natural calls tied to ES, and I will almost certainly take the bet.
You're arguing microstructure, which is absurd. It's more likely the natural will outperform the synthetic due to microstructure, unless you're a local.