b. A stock price is currently $30. During each two-month period for the next four months it is expected to increase by 8% or reduce by 10%. The yield curve is flat, and the risk-free interest rate is 5% per annum, continuously compounded.

(b1) Use a two-step tree to calculate the value of a European-style derivative, which is called power option, that pays off [max(30 ST , 0)]2, where ST is the stock price in four months.

(b2) If the derivative is American style, should it be exercised early?