Why Is the Delta of an ATM Option Most Sensitive to Changes in Implied Volatility?

The Delta of an At-the-Money (ATM) option is most sensitive to changes in implied volatility (IV) because ATM options are at the point of maximum uncertainty regarding their final outcome. A small change in IV significantly alters the probability distribution, immediately affecting the likelihood of the option expiring In-the-Money (ITM).

For deep ITM or OTM options, a change in IV has a smaller effect on Delta because the option's moneyness already dictates a high or low probability of ITM expiration. This high sensitivity is measured by the option Greek 'Vanna'.