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Does Early Exercise Always Result in a Loss for the Option Writer?

No, early exercise does not always result in a loss. The writer has already received the premium, which offsets the loss on the underlying transaction.

If the option is exercised deep-in-the-money, the writer incurs a loss on the position, but this is a realized loss, not necessarily a total loss, and is often managed through hedging. The writer's maximum profit is always the premium received.

What Is the Option Seller’s Maximum Profit?
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What Is the Maximum Profit for the Writer of Any Option Contract?
Does the Option Writer Calculate Profit Differently?