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Why are American put options more valuable than European put options?
American options can be exercised in advance, while European options can only be exercised at maturity. These two different methods show that the power of the United States is actually a little greater, so the value of American options is higher than that of European options.

For options without income assets, it can also be applied to American call options, because it is not advisable for American call options to be executed in advance without income, and the option execution date is also the expiration date, so BS applies American call options. For the American bearish, because it can be executed in advance.

Extended data:

(1) American option contracts can be performed at any time before or after the expiration date, and the settlement date is one or two days after the expiration date. Most American option contracts allow the holder to perform at any time between the trading day and the performance date, but some contracts stipulate a relatively short period, such as "two weeks before the expiration date".

(2) The European option contract requires its holder to perform the contract only on the due date, and the settlement date is one or two days after the performance. Domestic foreign exchange option trading adopts European option contract.

Baidu Encyclopedia-American Options