Final answer:
Exercising an American option before expiration results in the loss of its time value, which represents potential profit or insurance remaining until the option's expiration date.
Step-by-step explanation:
When you exercise an American option before the expiration date, the significant concept you give up is the time value of the option. This is because an option's price is composed of both intrinsic value and time value. The intrinsic value is what the option would be worth if it were exercised immediately, whereas the time value represents the potential for additional profit based on the time remaining until expiration. By exercising early, you may be losing potential upside or insurance value that could occur during the time remaining until the option’s expiration.