Suppose one can do delta hedging in a perfect way, that is, delta hedged tick by tick (suppose the tick space is very small, such as 0.000001 cent), no commission evolved, can one be guaranteed to obtain the option premium if he sells a call or put option regardless whether the implied volatility is higher or lower than actual volatility?
It's easier than that - just buy and sell the stock every time it crosses the strike back and fourth. Guaranteed winner!
why no? the option price is determined by stock price, strike price, volatility and time duration. since strike price and time duration are fixed, if we can hedge flawlessly to filter out the influence of the stock price, the option price is determined by volatility. the volatility exerts its influence on price by the movement of the stock price, since the stock price is hedged, thus the realized volatility has no influence on option price. in that way, we can pocket the part of option premium derived from volatility and time decay.
You don't know what you're talking about. Read Merton. You think the shit is majik. If you buy a 40-line and realized comes in at 45% you're going to earn that edge if you've hedged discretely and perfectly with no comms. Simulate it with some OTM puts on SPX. We'll wait.
I hope you don't trade options. If you asume basic BSM model, you hopefully realize that it's a no arbitrage portfolio of two components: 1. the option 2. replica of the option via underlying trades. So if statistical vol realized by underlying trades is larger than the option premium, you win if you're long the option and hedge delta and you lose vice versa. I'm not sure were you got the idea that realized vol has no influence on option price... Second, it's just impossible to do a perfect hedge since you have jump risk (overnight gaps), slippage and fees. Third, read and try to understand the PDF posted by @Kevin Schmit
Further, comms and zero (less regulatory) and all you're doing on vol is the initial premium. Trade ATM in SPX and hedge with SPY. You'll get absolutely brutalized trading the OTM so I don't think it's necessary to do so to prove my point.