Hi, So, I know that in theory, if you on a daily basis delta-hedge a short option position with a long future (or vice versa)... and then daily realized volatility happens to match the implied volatility perfectly... you would've ended up with a neutral position. No gain or loss overall. What about the math, if you're working with a delta-neutral strangle? If I have a delta-neutral strangle on day 0, and then adjust the strangle based on the closing price of day 1, and then day 2, day 3, etc.... and if realized volatility matches implied volatility... is the same true? Would there be no gain or loss overall? Or... can I just think of the strangle as two different option positions, with delta-hedges in the underlying that happens to exactly offset?
Assuming a perfect BSM world (i.e. flat vol), all options are created equal in terms of their replication characteristics. So any individual option or a combination of options behaves the same way. Obviously, the further you get from a perfect BSM environment, the more things start behaving differently.