Do All Stocks Offer Stock Options?

Not all stocks have stock options traded publicly in the exchanges. Stocks that offer publicly traded stock options in the exchanges for option trading are called Optionable Stocks.
The following are 4 criteria a company must meet in order for their stock options to be traded publicly in the option exchanges:

1. The stock must be listed on the NYSE, AMEX or Nasdaq.
2. The company must have >= 2,000 shareholders.
3. The company must have >= 7 million publicly held shares.
4. The closing price must have a minimum per share price for a majority of trading days during the three prior calendar months. (Note: Therefore, a company that had just launched its IPO has to wait for at least 3 months to have its options publicly traded in the exchanges, provided that it also fulfills all the other criteria).

Source: Investopedia