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Why Is the Extrinsic Value Highest for ATM Options?

The extrinsic value is highest for ATM options because they have the highest uncertainty regarding their final outcome. ATM options are precisely at the point where the underlying price can move either way, making them ITM or OTM.

This maximum uncertainty translates into the highest probability component (time value and volatility value), which is the extrinsic value.

Why Do ATM Options Have the Highest Time Value?
Why Do ATM Options Have the Highest Extrinsic Value?
Why Is Gamma Highest for At-the-Money Options?
Why Do ATM Options Generally Have the Highest Time Value?