I am reading page 126 (Chapter 8) of the book "Option Volatility and Pricing 2E" by Sheldon Natenberg and have two questions I seem to be stumped on. (The bulleted text below the charts in the screenshots are my own notes.)
Why is it that in making discrete adjustments to remain delta neutral, the variance of our P&L is "smoothed out"? (as described in 1st photo)
In calculating the total theoretical profit, how do the small profits from the unhedged portions (2nd photo) add up to the total options' theoretical value? Moreover, is my interpretation of how we are making $$$ through these mismatches correct? (3rd photo) I can see how, if after we sell the underlying at a higher price to offset positive delta exposure after an increase in the underlying, we then buy back the underlying at a lower price to reestablish our hedge, yields a profit... but am having trouble understanding which interpretation Natenberg is alluding too with the visual graph. Where is the profit coming from exactly / how are we so-called "capturing" value?