What is Asian Option?

Legal Definition
An Asian option (or average value option) is a special type of option contract. For Asian options the payoff is determined by the average underlying price over some pre-set period of time. This is different from the case of the usual European option and American option, where the payoff of the option contract depends on the price of the underlying instrument at exercise; Asian options are thus one of the basic forms of exotic options. There are two types of Asian Fixed Strike option, the Asian Fixed Strike call and the Asian Fixed Strike put. In general they do not differ in definition, only in how the pay-off is calculated.

One advantage of Asian options is that these reduce the risk of market manipulation of the underlying instrument at maturity (Kemna & 1990 1077). Another advantage of Asian options involves the relative cost of Asian options compared to European or American options. Because of the averaging feature, Asian options reduce the volatility inherent in the option; therefore, Asian options are typically cheaper than European or American options. This can be an advantage for corporations that are subject to the Financial Accounting Standards Board (2004 & FASB) revised Statement No. 123, which required that corporations expense employee stock options.
-- Wikipedia
Legal Definition
A COMPLEX OPTION that grants the buyer a payoff based on the geometric or arithmetic MEAN price of the UNDERLYING reference over a predetermined averaging period (i.e., ASIAN TAIL). The payoff can be determined by applying the average path to the price of the underlying (AVERAGE PRICE OPTION) or the STRIKE PRICE (AVERAGE STRIKE OPTION). Also known as AVERAGE OPTION.