An option with a payoff that depends on the average price of the underlying asset during at least some portion of the life of the option is called asian option.
Asian Option
As opposed to normal options (American and European), which base their reward on the price of the underlying asset at a certain moment in time, Asian options base their payoff on the average price of the underlying asset over a specified period of time (maturity). With these options, the buyer can buy (or sell) the underlying asset at the average price rather than the current market rate. Average options are another name for Asian options. The word "average" might be interpreted in a number of different ways, and the options contract needs to make that clear. The average price is typically an arithmetic or geometric average of the price of the underlying asset over a range of time intervals that are also defined in the options contract.
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