An Asian Option is based on the average price of the underlying asset over the life of the option and not a set strike price. Asian options are often used as they more closely replicate the requirements of firms exposed to price movements on the underlying asset. For example, an airline might purchase a one year Asian call opton on fuel to hedge its fuel costs. The airline will be charged the market rate for fuel throughout the life of the option and so an Asian option based on the average rate during the period would be preferable to an option based on a single strike price.
The average can be either the Arithmetic Average (ie the standard mean) or the Geometric Average (which is the mean when assuming all price moves are in percentages not absolute values).
The only extra input required in addition to the black scholes inputs is the Existing Average which is the average to date of the underlying price (if the option is being valued at its inception then this is set equal to the spot price)
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