The theory of delta hedging a short position in an option is based on trades in the stock and cash. I.e. I get the option premium and take positions in the stock and cash.
In the classical no-arbitrage theory I have the following if I am short an option, get the premium and hedge the structure with the stock: $$ maketvalue(stock trading) + premium received = marketvalue(option) $$ which is equivalent to $$ maketvalue(stock trading) = marketvalue(option) - premium received $$ where I assume zero interest rates.
Thus if I just Delta hedge an option that I did not short, thus the premium of which I did not receive, then the relation must be the same as the lhs does not change.
Thus if I want to "generate an option payoff" I just trade the underlying:
$$ maketvalue(stock trading) = marketvalue(option) - premium received $$
If I do this with futures then all costs must be included in the pricing of futures and the margin payments.
Summing up: replicating the option without actually trading it, I will replicate it "minus" the premium ... I will get less than the pay-off.
What happens if I do the hedge with futures? Then I don't need cash (except for the margin account).
To ask the question differenetly: if I replicate a put or a call with futures can I make money (the pay-off) from nothing? Obviously not: I will miss the option premium. Furthermore I have a hedging error and additional risk (basis risk as Freddy mentions).
Is there anything more that I miss in this thought? Is the premium and the hedging error the only difference?