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What Is the Concept of ‘Early Exercise Premium’ in American Options?

The early exercise premium is the extra value an American option has over its European counterpart due to the ability to exercise before expiration. It is the difference between the American option's price and the European option's price.

This premium is typically small for non-dividend-paying assets, but it exists because the flexibility to exercise early can be used to capture a dividend or to reinvest capital sooner, making the American option intrinsically more valuable.

Does the Early Exercise Feature of American Options Increase or Decrease the Premium, and Why?
Does an American Put Option on a Non-Dividend Paying Stock Ever Benefit from Early Exercise?
Under What Specific Conditions Is It Rational to Exercise an American Call Option Early?
Under What Circumstances Would an Early Exercise of an American Option Be Beneficial?