Problem 2: (10 marks) A derivative on a stock will expire exactly 6 months from now. The payoff of the derivative is given by: Payoff =ST120 if ST120 =2ST240ifST>120 where ST denotes the price of the stock on the expiry date. The stock price today is 100 . On the expiry date, the stock price is expected to be either 150 or 80 . The annual interest rate is 10% and compounded continuously. Using a two period model, find the price of the derivative. Explain all your steps clearly