An Asian option (also called an average option) is an option whose payoff is linked to the average value of the underlier on a specific set of dates during the life of the option. There are two basic forms:

An average rate option (or average price option) is a cash settled option whose payoff is based on the difference between a the average value of the underlier during the life of the option and a fixed strike.

An average strike option is a cash settled or physically settled option. It is structured like a vanilla option except that its strike is set equal to the average value of the underlier over the life of the option.

Both forms can be structured as puts or calls. Exercise is generally European, but it is possible to specify early exercise provisions based upon an average-to-date. Averages can be calculated arithmetically:

or geometrically: