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:
There are also exotic options, which are exotic because there might be a variation on the payoff profiles from the plain vanilla options. Or they can become totally different products all together with "optionality" embedded in them. For example, binary options have a simple payoff structure that is determined if the payoff event happens regardless of the degree. Other types of exotic options include knock-out, knock-in, barrier options, lookback options, Asian options, and Bermudan options. Again, exotic options are typically for professional derivatives traders.
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.
A long options trade is entered by buying an options contract and paying the premium to the options seller. If the market then moves in the desired direction, the options contract will come into profit (in the money). There are two different ways that an in the money option can be turned into realized profit. The first is to sell the contract (as with futures contracts) and keep the difference between the buying and selling prices as the profit. Selling an options contract to exit a long trade is safe because the sale is of an already owned contract.
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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