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: $$ \rm Market Value (stock \, trading) + Premium Received = MarketValue(option) $$ which is equivalent to $$ \rm MarketValue(stock \, trading) = MarketValue(option) - Premium \, Received $$ where I assume zero interest rates.
Thus if I delta hedge an option that I did not short, the premium of which I did not receive, then the relationship must be the same as the left hand side of the equation does not change.
If I want to "generate an option payoff", I trade the underlying:
$$ \rm MarketValue(stock \, trading) = MarketValue(option) - Premium \, Received $$
If I do this with futures then all costs must be included in the pricing of futures and the margin payments.
To summarize: Replicating the option without actually trading it, I will replicate it "minus" the premium ... I will get less than the pay-off. Is this correct?
What happens if I do the hedge with futures? Then I don't need cash, except for the margin account.
To ask the question differently: 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).
Is there anything that I missed? Is the premium and the hedging error the only difference?