2. A stock price is currently 30. Over each of the next two 3-week periods it is expected to increase by 10% or decrease by 8%. The risk-free interest rate is 6% per annum with monthly compounding during the first 3-week period and 4% per annum with weekly compounding during the second 3-week period. (a) Write an R program that gives the binomial tree evolution of the stock price. [3 marks] (a) Write an R program to find the initial price of a derivative that pays off max((900 S (T)), 0). [5 marks] (a) If the derivative is American-style, what is its initial value? should it be exercised earlier? Justify your answer [5 marks] (a) Write an R program to find the initial price of a lookback call option with fix strike K = 31. [5 marks] Hint: Recall that the payoff of a lookback call option with fix strike is given by: max(max S(i) - K, 0) 0