Suppose you own 100 shares of IBM, which on 23 August sold for $161.30 per share.
You could sell someone the right to buy your 100 shares at any time during the next five months at a price of $165 per share. The $165 is called the strike price, or exercise price.
This is defined as a “called option” because the purchaser has a “call” on 100 shares of the stock.
The seller is called “the option writer”.
Such options exist and are traded on exchanges. Chicago Board Option Exchange (CBOE) is the oldest and largest one.