To further reduce the underlying volatility, Bilal Aslam and Changyong Zhang (2022) introduced the average-Asian option.

**Definition**

An option is called an average-Asian option if the payoff equally depends on

- the average price of the underlying asset during the life of the option, and
- the mean of the underlying price at expiry and the strike price.

The payoff of an average-Asian call option is

and that of an average-Asian put option is

where is the underlying price at expiry t=T, is the average price of the underlying asset from time t=0 to t=T, and K is the strike price.

**Reference**

Bilal Aslam & Changyong Zhang (2022): A strengthened solution to option manipulation, INFOR: Information Systems and Operational Research, DOI: 10.1080/03155986.2022.2044222