Since many people are buying and selling options all over the world on any given day, there are "option exchanges" where options are traded just as stocks are traded. Assuming that the stock you want to sell an option on is one that other investors will want to own (i.e. one that inspires "open interest"), you should have no difficulty in selling your option.
There are 5 major exchanges where options are traded:
1. Chicago Board of Option Exchange
2. American Options Exchange
3. Pacific Exchange
4. Philadelphia Exchange
5. New York Options Exchange
Buying and selling options is just the same as buying and selling stocks. Option transactions are always conducted through a broker, who buys or sells options through the traders who are on the floor of the options exchange. You, the investor, don't know (or care) who buys the option. To repeat a fundamental point, it is important to realize that when you sell an option it is sold through an exchange where options are being traded every day.
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