it is expected to increase by 10% or decerease by 8%. The risk-iree interesest rate 1\% per annum with reekly compounding duing the second 3 rreek period. (a) Write an R proogram that gives the binomial tree erolution of the stock price. [3 marks (a) Witte an R proogram to find the initial price of a derivative that pars off max(41(000S2(T)),0). |5 marks (a) If the derivative is American-style, what is its initial value? should it be exerciced eatlier?? Justify your anstre? [5 marks (a) Witte an R program to find the initial price of a lookbadk call option with fix strike K=31. |5 marks Himt: Recal that the payof of a lookbadk call option with fix strilke is given by: max(maxS(i)K,K,0)