An Asian option pays the maximum of either 0 or the difference between the final stock price and the average stock price along the relevant price path. For example, assume that the price path is 100, 80, 100. The average price is 280/3, and the option would pay (100-(280/3))=20/3. If the price path is 100, 125, 100, the average price is 325/3, and the option would pay 0.
So given all this, you have an Asian option that expires in 2 periods where the stock price in period 0 is 90. The stock either moves up with u=1.15, or down with d=1/1.15. The interest rate is 1/19. What is the value of your option today in period 0?