In practice, how do people usually delta hedge options the day before expiry? Would you still use the black Scholes delta and then close out the position in the underlying immediately after expiry? After all, the day before expiry the option becomes "binary" in some sense, I.e. it expiries either ITM or OTM. For strikes that are more than 3 daily standard deviations away from spot, the BS delta would anyway be close to 0 or 1, but how about strikes closer to spot?
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$\begingroup$ This question has been asked before but IIRC with no definite answer other than "that's a difficult situation, because of the large gamma". $\endgroup$– nbbo2Aug 24, 2021 at 9:10
$\begingroup$ Fundamentally there is no difference. It does not matter if there is 1, 2, 3 or any other time to expiry. Many systems compute delta also on the day of expiry (with minutes to expiry). As long as you have exposure, you may want to hedge. How frequently you do that, is probably more art than science (in a strict theoretical sense it should be "all the time"). $\endgroup$– AKdemyAug 24, 2021 at 21:41
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