American options can be exercised at any time between the date of purchase and the expiration date. European options are different from American options in that they can only be exercised at the end of their lives on their expiration date. The distinction between American and European options has nothing to do with geography, only with early exercise. Many options on stock indexes are of the European type. Because the right to exercise early has some value, an American option typically carries a higher premium than an otherwise identical European option. This is because the early exercise feature is desirable and commands a premium.
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In, At, or Out of the Money: If an option is in the money, its premium will have additional value because the option is already in profit, and the profit will be immediately available to the buyer of the option. If an option is at the money, or out of the money, its premium will not have any additional value because the options are not yet in profit. 
Sometimes corporations enter the forex market in order to hedge their profits. A US company with extensive operations in Mexico, for example, may enter into a futures contracts on US dollars. So, when it comes time to bring those Mexican profits home, the profits earned in pesos will not be subject to unexpected currency fluctuations. The futures contract is a way of securing an exchange rate and eliminating the risk that peso will lose value versus the dollar, making those profits worth less in dollars.

An option is a contract that allows (but doesn't require) an investor to buy or sell an underlying instrument like a security, ETF or even index at a predetermined price over a certain period of time. Buying and selling options is done on the options market, which trades contracts based on securities. Buying an option that allows you to buy shares at a later time is called a "call option," whereas buying an option that allows you to sell shares at a later time is called a "put option."