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The real question is: does Benn use numerical delta or black-scholes delta for his delta hedging. Bonus points if you know the difference!
By numerical delta you mean bumping the stock px and and implied vol (using a model for change in iv when stock moves) and computing a delta from that - to get something like a skew delta?
yes. BS delta just uses whatever vol is at that point, numerical uses vol as a function of spot and strike so you use different IV when doing f(x+h)-f(x) / h
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