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When purchasing put options, you are expecting the price of the underlying security to go down over time (so, you're bearish on the stock). For example, if you are purchasing a put option on the S&P 500 index with a current value of $2,100 per share, you are being bearish about the stock market and are assuming the S&P 500 will decline in value over a given period of time (maybe to sit at $1,700). In this case, because you purchased the put option when the index was at $2,100 per share (assuming the strike price was at or in the money), you would be able to sell the option at that same price (not the new, lower price). This would equal a nice "cha-ching" for you as an investor.
Now, think of a put option as an insurance policy. If you own your home, you are likely familiar with purchasing homeowner’s insurance. A homeowner buys a homeowner’s policy to protect their home from damage. They pay an amount called the premium, for some amount of time, let’s say a year. The policy has a face value and gives the insurance holder protection in the event the home is damaged.
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.
The price at which you agree to buy the underlying security via the option is called the "strike price," and the fee you pay for buying that option contract is called the "premium." When determining the strike price, you are betting that the asset (typically a stock) will go up or down in price. The price you are paying for that bet is the premium, which is a percentage of the value of that asset. 
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