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Why Is the Premium Generally Higher for an American-Style Option than a European-Style Option?

The premium is higher because the American-style option grants the holder an additional right: the right to exercise early. This added flexibility, or optionality, has a monetary value.

Since the seller (writer) takes on a greater risk of being assigned early, they demand a higher price, known as the premium, to compensate for this increased uncertainty and risk exposure.

Why Might an American Option Have a Higher Premium than a European Option?
What Is the Concept of ‘Early Exercise Premium’ in American Options?
Does the Early Exercise Feature of American Options Increase or Decrease the Premium, and Why?
Why Are European-Style Options Generally Simpler to Price than American-Style Options?