How does an option start to exist?
Option is a derivative security and, said in the most general way, option is a contract. It is a contract between the buyer and the seller of the option.
Buyer agrees to pay a price to the seller (the market price of the option at the time of buying it) and for that price he gets the possibility (the choice or… the option) to buy (if it is a call) or sell (if it is a put) a defined quantity of a defined security (the underlying) for a defined fixed price (the strike price). The buyer has the right to exercise the option, but not the obligation.
On the other hand, the seller has an obligation to sell the underlying to the call option’s buyer (or to buy the underlying from the put option’s buyer), if the owner of the option decides to exercise. This is the contract, the agreement between the buyer and the seller of the option. At the moment they make this agreement, the option starts to exist.
How does an option cease to exist?
Options generally have limited life. The buyer’s right to exercise does not last forever, but it is constrained to a time period specified in advance. In other words, every option has a fixed expiration date. After this date has passed, the option is not valid any more and the buyer no longer has the right to exercise.
There are two ways how an option can cease to exist. It can be exercised by the option’s owner (the buyer) or if it is not exercised until or at the expiration date, the option expires.
American vs. European options
There are two kinds of options. American options can be exercised any time during their life. If you own an American option, you can exercise it any time from the moment you buy it until its expiration date.
European options, on the contrary, can be exercised only exactly at the moment of their expiration.
Note that the names have nothing to do with the places where these options trade. There are both kinds of options (American and European) trading in America and also both kinds trading in Europe. These two kinds of options are also traded in other parts of the world, but they are still called American and European. It is about when it can be exercised and not about the location.
Exercising the option
How do you exercise an option? Let’s say you own an American call option on Microsoft stock, which gives you the right to buy Microsoft stock for 20 dollars (this is the strike price). Microsoft stock is trading at 25 and the option’s intrinsic value is 5 dollars. The expiration date is approaching and you decide that you want to exercise the option before it expires and becomes worthless. It is a good idea, because by exercising the option you can buy Microsoft stock for 20 dollars (the strike price) and you can immediately sell the stock in the stock market for 25. You make 5 dollars profit on this.
So you want to exercise the call option. You must notify the seller of the option of your intention (in practice you usually notify your broker) and the seller has an obligation to sell you the Microsoft stock for 20 dollars (while it trades at 25 in the stock market). This way the seller loses 5 dollars, which equals your profit. Options are a zero sum game; the profit or loss of the buyer and seller are exactly inverse.
After you have exercised your option and you got the stock, you no longer have the option, as the option has ceased to exist by being exercised.