I am trying to understand an option PnL coming from vega and gamma better.If implied vol (IV) is much higher than realized vol (RV) and assume i expect them to converge (without knowing whether IV will drop or RV will rise). Suppose I sell an option and delta hedge it. Staying with Black framework, my daily PnL is roughly vega * Change(IV) + 1/2 * gamma * (RV*RV - IV*IV). Both vega and gamma are negative.So if IV drops but still stays above RV, then i make money from both terms.If IV drops below RV, then the 2 terms have opposite sign and i may make or lose money.If IV stays constant and RV increases (but stays below IV), i make money from gamma.If IV stays constant and RV rises above IV, i lose money from gamma. Are the above statements correct?Thanks for any insight.

I think the gamma term is wrong. It's more like 1/2 * gamma * (RV^2 - IV^2) * S^2 where S is the underlying price. Also since you include gamma, you should add a theta term too. When you have a large gamma, you often have a large theta to work against the gamma term. Also, to calculate greeks, you need to input a volatility number, the choice of IV or RV also affects your pnl.

you can sell an option at a very high implied vol and delta hedge while the actual realized vol is much lower and still lose money.all you need is just a few days of high volatility when your gamma is very high. what matters is the gamma weighted realized volatility.

on the topic of realised volatility, is it then possible to calculate the gamma profits locked in til date from just looking at my hedges?eg i am delta hedging a long call position, and i sold 100 lots at $70 on day 0, then bot back 10 lots at $68 on day 1, etc.. (assuming i/r = 0)....else, using the formulation of 0.5*gamma*RV^2 * S^2 * dt.... and i am on day 1, how do i compute this RV based on the hedges i managed to lock in? (68-70)/70 and then annualised it and call it as RV?

On a slight tangent, I thought about doing this a while ago, but the concern is that Realize Vol and Implied vol do not necessarily need to converge. It could be that implied vol is consistently higher than realized vol for nearly a decade, and you'd be making money with incredibly low PnL volatility.People postulated that the reason is that Implied vol is at a premium to Realized Vol because of default risk and other systematic risks that will not be reflected in the Realized Vol. Sounds great at first.Having said that, if you looked at the Merrill Lynch Equity Implied Vol Arbitrage index (MLHFEV1 on Bloomberg) which is pretty much this strategy, if you had started this arbitrage 10 years ago in '99, you'd be way in the black all the way up until oct of '08, then you'd give it all back and be in the red within 2 months and barely break even as of this week.But suppose the bad is in the past, anyone have any thoughts on what the optimal hedge frequency for such a strategy would be? maybe as a function of gamma or realized vol or other factors?