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In a backtest I did, I'm selling a call option and buying a delta amount of the underlying (calculated using implied vol). Now I know in the limit case of continuous hedging I end up paying a PnL which is a gamma weighted integral of volatility differences, but in discrete hedging (daily) backtest, I'm getting slightly positive PnL's. I'm unable to reconcile this with an intuition. What must drive such a result?

I expect to lose PnL because implied vol seems to be consistently smaller than the realized vol (if calculated as sample standard deviation on a rolling basis)

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  • $\begingroup$ It's not a simulation, I'm not sure why it's been edited that way. It's a real backtest. Sorry if I am not on the same page. $\endgroup$
    – user121416
    Oct 4, 2022 at 14:41
  • $\begingroup$ Sorry, amended. $\endgroup$
    – nbbo2
    Oct 4, 2022 at 14:43
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    $\begingroup$ Could be several reasons. Such as implied was most of the time higher than your realized in the backtest. Also, I don't know if you updated the implied vol daily or just hedged with the same IV until maturity, but if you did update your IV used in your hedge daily, then actually your P&L also contains contribution from Vega vanna and Volga which may have worked in your favour. It's difficult to precisely pinpoint unless you carry out a detailed P&L attribution. $\endgroup$
    – user34971
    Oct 4, 2022 at 15:49
  • $\begingroup$ @FridoRolloos the delta hedge is always with the same IV, I am not marking to market. $\endgroup$
    – user121416
    Oct 4, 2022 at 22:20

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