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What Happens to the Option’s Time Value Immediately after an Early Exercise?

The option's time value immediately drops to zero. When the option is exercised, the contract ceases to exist, and all future potential for price movement is eliminated.

The holder realizes only the intrinsic value, and the time value, which represents the remaining uncertainty and potential, is forfeited.

What Is the Concept of ‘Early Exercise Premium’ in American Options?
How Does the Time Value Component of an Option Premium Relate to the Early Exercise Feature?
What Is the Opportunity Cost of Exercising a Deep In-the-Money American Call Option Early?
Does the Underlying Asset’s Volatility Influence the Decision to Exercise an American Option Early?