How do options work?

I thought it was if the price goes up you have the option to buy shares at the old price. But if the share price goes down, you have the option of not buying.

Cashing them in is simply selling the right to someone else. Or is it buying at the old price and immediately selling at the new higher price? This year your option is worthless so you can't sell it and you don't want to buy your shares for more than the current market price. The only way you can owe the company money is if you foolishly opt to buy the shares anyway even though the price you pay is higher than market price.

But I could be wrong.