More Specific Follow-Up Option Question?

Say company XYZ has a total of 100 shares outstanding. Current market price is 30. Say banks, investors, the Options Clearing Corporation, The American Stock exchange, and/or The Chicago Board of Investors (I don't know who writes options) write over 100 calls to accommodate different market conditions and strike prices respectively. For this example, the average for these hypothetical calls is 35. If there are over a hundred calls, some have to be naked or uncovered, right?

Let鈥檚 say the market price of the sock increases to 60 and everyone who purchased the calls decides to exercise them. What happens? Can this happen, a lack of underlying securities? How is this prevented? Who is responsible? That is why I don't understand how options are initially issued and who issues them. And that is my main question: Who issues the options innitially and how do they have that ability?

Options are a zero sum game. For ever winner, there is a loser.
Most options are settled in cash and not exercised for the underlying stock. Options are purchased to either speculate in a movement (up or down) in a stock or to hedge a position. One of the incentives to buy an option is the leverage it produces. The increased leverage increases the potential gain. Exercising the option (if you are ahead) essentially reduces the leverage and is somewhat counterintuitive.
The OCC has rules to prevent unusual situations such as your hypothetical and can decide how settlements are handled. For example, if everyone wanted shares delivered and there were not enough available (on deposit in the accounts of those who sold the option), the OCC could decide that some holders would have to accept cash settlement instead of shares. The exchanges have surveillance teams that watch for unusual trading and situations, and can make adjustments (limiting naked options or increasing margin). The created the option contracts and the rules for how they operate.

Most companies have millions of shares of outstanding, publicly traded stock, yet there aren't usually that many option contracts outstanding. Before options can be listed on a stock, one of the criteria is that the stock have adequate liquidity, so that the type of imbalances that you ask about are not likely to occur.
Naked or uncovered situations can occur but the function of the OCC and the Exchanges is to insure that each side of the option trade has the ability to settle their obligation, usually through the requirement that margin be posted. Usually brokerage firms will not allow account holders to be uncovered unless sufficient margin is posted or the total account value is enough to be liquidated to make good on the account holder's obligation. If not, the brokerage firm could be held responsible for making good on its account holder's obligation.

Options are issued by the Options Clearing Corporation
The OCC, AMEX, do not write options they are exchanges, (or market placesl thefore they do not trade)

OCC will not issue option contracts for any publically traded company that exceed the total amount of stock outstanding

"how do they have that ability" because they know what they are doing. technically all exchanges know how many shares their companies that are listed with them have outstanding, therefore they know how many contracts can be issued. There was a data base with this info that was used by OCC