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Im quite confused. As I understand from standard delta PNL of option + underlying position, pnl is equals to difference between realized and implied vol weighted by gamma.

However, as I understood, implied in that formula - is basically what you paid (got paid) at the start of the options life, meaning that you basically bet on realized vol on the whole life of an option.

How can then realized prediction for shorter intervals (like 1-7 days) help then in delta hedging pnl for an option of 1-2 month for example?

Thanks!

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