Option is a kind of a contract that gives you right (with no obligation to do so) to buy (call option) or sell (put option) a specified amount of shares of an underlying stock by a specified strike price. The contracts are usually have expiration date after which the right is voided.
Options give you control over a subject (usually stock). For example, you are going to buy a car which is claimed to be a third car of H. Ford. However, instead of buying the car itself (for $100K) you are buying call option for $2K which gives you right to buy this car for $100K. If expertise shows this car was first one and its price goes up to $200K you still can own it for $100K. Otherwise, if expertise shows that it is a piece of junk you are loosing just $2K.
Options give you derived access over a company shares. This means that a price of an option itself trends to a price of a stock minus strike price in case of call contracts and plus strike price in case of put contracts. That is correct for close expiration dates and less accurate for contracts that are further to expire.
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