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enter image description here if you're long OTM calls, an increase in vol would increase your delta (converges to ATM) and if you're long ITM calls, increase in vol would decrease your delta (converges to ATM as well). So OTM calls have positive DdeltaDvol (Vanna) and ITM calls have negative Vannas. Following Nassim's example, if you're short OTM (below the money) calls and long ITM (above the money call) the book must have positive DdeltaDvol and not negative.

enter image description here This is a Vanna graph from Natenberg's book to present a visual of the above. Can anyone please confirm this?

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  • $\begingroup$ Without further context it is hard to tell if the author was right or wrong. Apart from that: it is straightforward to take two BS formulas and figure out what is going on. I hope you don't want us to do that. $\endgroup$
    – Kurt G.
    Mar 25, 2023 at 8:52

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You’ve probably figured this out by now. But you’re confusing OTM calls with below the money calls. An OTM call is above the money, not below.

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