Average-Asian Option

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

$\frac{1}{2}max(A_T-K+\frac{S_T+K}{2}-K,0)=\frac{1}{4}max(2A_T+S_T-3K,0)$

and that of an average-Asian put option is

$\frac{1}{4}max(3K-(2A_T+S_T),0)$

where $S_T$ is the underlying price at expiry t=T, $A_T$ 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