I'm new, haven't made any trades yet. want to know this from the brokers point of view. He has to supply me with a stock at the strike price if I choose to exercise the option. Say the contract is for $10 and now the stocks value is up to $15. How does the broker go about buying the stock for me at $10 when the market is now costing him $15 to purchase it? Is he paying the $5 difference out of his own pocket? Or does he procure it in some way for $10?
The option seller (also known as option writer) is the one who will give you the stock at $10. Most of the time he already has the stock (so for him it is a covered call). Otherwise he will of course have to buy at $15 and deliver it to you at $10 per share ($5 loss per share for him), if you choose to exercise your option.
The broker is not the one writing contracts that you buy. That would be a serious conflict of interest anyhow..
The broker provides a service to you. He shops your order to a market maker who will sell you the option. The market maker hopes to buy the option from another customer and pocket a spread or he will hedge the risk out. If he can't buy the option somewhere else, he will probably hedge out the option (reduce or eliminate his exposre to stock price movements). This is done by buying some stock today at $10. If he chooses not to hedge then he will be forced to buy stock at $15 in the open market to deliver to you at expiry.