What Is the Relationship between Vanna and the Concept of “Sticky Delta”?

The concept of "sticky Delta" suggests that when the underlying price moves, the implied volatility for a given Delta level tends to remain constant. Vanna measures the change in Delta for a change in volatility.

If Vanna is zero, it means Delta is not changing with volatility, which supports the sticky Delta assumption. Therefore, a low Vanna is consistent with a sticky Delta model.