If there’s a company you’ve had your eye on and you believe the stock price is going to rise, a “call” option gives you the right to purchase shares at a specified price at a later date. If your prediction pans out you get to buy the stock for less than it’s selling for on the open market. If it doesn’t, your financial losses are limited to the price of the contract.
If in six months the market crashes by 20% (500 points on the index), he or she has made 250 points by being able to sell the index at $2250 when it is trading at $2000—a combined loss of just 10%. In fact, even if the market drops to zero, the loss would only be 10% if this put option is held. Again, purchasing the option will carry a cost (the premium), and if the market doesn’t drop during that period, the maximum loss on the option is just the premium spent.
A longer expiration is also useful because the option can retain time value, even if the stock trades below the strike price. An option’s time value decays as expiration approaches, and options buyers don’t want to watch their purchased options decline in value, potentially expiring worthless if the stock finishes below the strike price. If a trade has gone against them, they can usually still sell any time value remaining on the option — and this is more likely if the option contract is longer.
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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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.
Of course, many investors, especially new investors, are skittish about options. After all, no investor is required to trade this way, and the transactions can seem complicated. But once you know the pros and cons of this type of investing, it can be a powerful part of your strategy. No investors should be sitting on the sidelines simply because they don’t understand options.
Conversely, a put option is a contract that gives the investor the right to sell a certain amount of shares (again, typically 100 per contract) of a certain security or commodity at a specified price over a certain amount of time. Just like call options, a put option allows the trader the right (but not obligation) to sell a security by the contract's expiration date. 
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