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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.
With straddles (long in this example), you as a trader are expecting the asset (like a stock) to be highly volatile, but don't know the direction in which it will go (up or down). When using a straddle strategy, you as the trader are buying a call and put option at the same strike price, underlying price and expiry date. This strategy is often used when a trader is expecting the stock of a particular company to plummet or skyrocket, usually following an event like an earnings report. For example, when a company like Apple  (AAPL) is getting ready to release their third quarter earnings on July 31st, an options trader could use a straddle strategy to buy a call option to expire on that date at the current Apple stock price, and also buy a put option to expire on the same day for the same price.
With this strategy, the trader's risk can either be conservative or risky depending on their preference (which is a definite plus). For iron condors, the position of the trade is non-directional, which means the asset (like a stock) can either go up or down - so, there is profit potential for a fairly wide range. To use this kind of strategy, sell a put and buy another put at a lower strike price (essentially, a put spread), and combine it by buying a call and selling a call at a higher strike price (a call spread). These calls and puts are short.  
Just as you can buy a stock because you think the price will go up or short a stock when you think its price is going to drop, an option allows you to bet on which direction you think the price of a stock will go. But instead of buying or shorting the asset outright, when you buy an option you’re buying a contract that allows — but doesn’t obligate — you to do a number of things, including:
Options are available as either a Call or a Put, depending on whether they give the right to buy, or the right to sell. Call options give the holder the right to buy the underlying commodity, and Put options give the right to sell the underlying commodity. The buying or selling right only takes effect when the option is exercised, which can happen on the expiration date (European options), or at any time up until the expiration date (US options).
The fee you are paying to buy the call option is called the premium (it's essentially the cost of buying the contract which will allow you to eventually buy the stock or security). In this sense, the premium of the call option is sort of like a down-payment like you would place on a house or car. When purchasing a call option, you agree with the seller on a strike price and are given the option to buy the security at a predetermined price (which doesn't change until the contract expires). 
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