Problem 3: Derivatives Valuation (6 marks) A stock price is currently $36. During each three-month period for the next six months it is expected to increase by 9% or decrease by 8%. The risk-free interest rate is 5%. Use a two- step tree to calculate the value of a derivative that pays off (max[(40-ST),0])2 where S, is the stock price in six months. e. If the derivative is of American style (St in the payoff function refers to the stock price when the option is exercised), should it be exercised early? [1 mark]