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.
Fluctuations in option prices can be explained by intrinsic value and extrinsic value, which is also known as time value. An option's premium is the combination of its intrinsic value and time value. Intrinsic value is the in-the-money amount of an options contract, which, for a call option, is the amount above the strike price that the stock is trading. Time value represents the added value an investor has to pay for an option above the intrinsic value. This is the extrinsic value or time value. So, the price of the option in our example can be thought of as the following:
Volatility: If an options market is highly volatile (i.e. if its daily price range is large), the premium will be higher, because the option has the potential to make more profit for the buyer. Conversely, if an options market is not volatile (i.e. if its daily price range is small), the premium will be lower. An options market's volatility is calculated using its long-term price range, its recent price range, and its expected price range before its expiration date, using various volatility pricing models.
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Options trading may seem overwhelming, but they're easy to understand if you know a few key points. Investor portfolios are usually constructed with several asset classes. These may be stocks, bonds, ETFs, and even mutual funds. Options are another asset class, and when used correctly, they offer many advantages that trading stocks and ETFs alone cannot.
In terms of valuing option contracts, it is essentially all about determining the probabilities of future price events. The more likely something is to occur, the more expensive an option would be that profits from that event. For instance, a call value goes up as the stock (underlying) goes up. This is the key to understanding the relative value of options.
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." 
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