There are two sorts of options. Company offered options are...

There are two sorts of options. Company offered options are issued to share holders however the company decides. EG one option to buy one new share for each share held...or sometimes one option to buy one new share for say, every 5 or 10 or 100 shares held..at a fixed price.

Exchange traded options.."The stock options Market" is an entirely different creature. It is a contract with another investor or deal maker to buy or sell a number of certain shares within a fixed time frame and at a contracted price, for which you pay a premium.
Dont confuse the two.