Could somebody explain the following to me:
Essentially, an approximative (ignoring higher-order terms) formula for the change in a call-price is computed. If we delta-hedge, then delta is set to 0, giving us the last formula.
Here's what I don't get: The $\Delta$ for the call is not zero. So you can't just set it to 0, right?
It's true that the "overall delta" is 0 .... but that's not equivalent to the $\Delta$ that appears in the first and second equations in the picture. So I don't see how the text can argue that the 'overall delta' is 0, which is true, and then proceed to set the Call's $\Delta$ equal to 0?
More generally, I am looking for the theoretical PnL formula for a simple delta-hedge where 1 call option is bought, and we short delta in the underlying.