Question 2 (15 marks) A stock is currently traded at $60. The standard deviation of the stock return is 30% per annum. The riskless interest rate is 5% per annum. The terminal payoff of the derivative is specified as: Payoff = 3ST + 10 (i) Suppose that the derivative is a knock-out option with one year remaining. The barrier is set at $80. Construct a four-step binomial tree to price this barrier option. (6 marks) (ii) Suppose that the derivative is a knock-in option with one year remaining. The barrier is set at $80. Construct a four-step binomial tree to price this barrier option. (6 marks) (iii) Suppose that the derivative is a normal European style option with one year remaining (i.e., it does not have the barrier). Without constructing a binomial tree, what is the price of this European option? Justify your answers. (3 marks)