With respect to an option, this cost is known as the premium. It is the price of the option contract. In our home example, the deposit might be $20,000 that the buyer pays the developer. Let’s say two years have passed, and now the developments are built and zoning has been approved. The home buyer exercises the option and buys the home for $400,000 because that is the contract purchased.
So, call options are also much like insurance - you are paying for a contract that expires at a set time but allows you to purchase a security (like a stock) at a predetermined price (which won't go up even if the price of the stock on the market does). However, you will have to renew your option (typically on a weekly, monthly or quarterly basis). For this reason, options are always experiencing what's called time decay - meaning their value decays over time. 
For example: A steel manufacturer importing coal from Australia currently and in order to reduce the volatility of changes in prices he always hedges the coal purchases on a 3 monthly forward contract where he agrees with the seller on day one of financial quarter to supply coal at defined price irrespective of price movements during quarter. So in this case, the contract is forward/future and buyer has an intention to buy the goods and no intention of making profit from price changes.
If a company locks in the price and the price increases, the manufacturer would have a profit on the commodity hedge. The profit from the hedge would offset the increased cost of purchasing the product. Also, the company could take delivery of the product or offset the futures contract pocketing the profit from the net difference between the purchase price and the sale price of the futures contracts.
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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.
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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