A corporation may grant someone the option to purchase a set number of shares of the corporation's stock at a price (the "strike price") fixed at or around the time the option is granted. The shares are set aside until a later date when the grantee may exercise the option to buy the shares--this event is called vesting. Options may vest all at once, or an option on part of the shares may vest periodically. The shares may be bought and held, like shares purchased through a stock exchange, or they may be immediately sold, hopefully for a profit.

Many companies grant employees stock options as an incentive to stay with the company for the whole vesting period, and to work hard to promote the company's success, increasing the value of the company and thus the price of its stock. This incentive is lost on employees of privately-held corporations, since it is nearly impossible to sell shares of stock purchased through these options. But they can be very enticing to employees of a publically-traded corporation, as the difference between the stock price and the strike price can reflect a substantial profit.

In the stock market, stock options are a time-limited right (but not an obligation), sold at a certain price, to perform a transaction with the issuer, the conditions of which are fixed and may therefore differ from the conditions the market would later dictate. See Options for the details, why this may be desirable but is dangerous.

Stock options are a much broader field than what linky describes. They are sold and bought just like the stocks themselves, by pretty much everyone. Nowadays, options are never actually exercised in the sense that the option holder actually buys the underlying stock (or bond, or currency, or commodity) at the expiration date - instead, he recieves the price difference between the strike price and the current market value from the issuer.

This type of financial derivative instrument was originally invented to provide (limited) security against falling prices for e.g. sugar cane to farmers, and (limited) security against rising prices to companies that e.g. produce and sell refined sugar. Then, it was (and still is) adapted in a similar manner by people dealing with stocks, for whom such concepts are natural, and eventually some of them, those with gambling mentalities, realized that the leverage that options provide makes it possible to very quickly make huge fortunes with very little starting capital - and then discovered that in the same way, it is possible to lose huge fortunes even more quickly.

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