A stock price is currently $50. During each 3-month period for the t 6 months it will increase by 7% or reduce by 12%. The risk-free merest rate is 6%. Use a two-step tree to calculate the value of a derivative that pays off [max (ST-43,8)12 where St is the stock price 6 months. The min formula in brackets simply means that you have to choose the minimum between ST-30 and 20 when valuating the option price at every node. Use a two-step binominal tree to solve this exercise.

a. Calculate the risk neutral probability

b. Draw a binomial tree. Calculate the expected stock prices and derivative prices at the terminal nodes.

c. Derive the value of the derivative if this is a European-style derivative.

d. If the derivative is American style, what would be the derivative's value? Should it be exercised early?