A non-dividend paying stock is currently trading at 42. Over each of the next two 3-month periods it is expected to either go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. Suppose there is a 6-month European put option with a strike price of 11. Answer the following questions (show all the details of your calculations and present your results with four decimal places) a) Draw a two-period binomial tree for the underlying asset. b) Calculate the price of the option today. c) Work forward on the tree and show that there is a self-financing trading strategy that replicates the value of the European put option at each node in the tree. d) Suppose the option is American. Calculate its price today. A non-dividend paying stock is currently trading at 42. Over each of the next two 3-month periods it is expected to either go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. Suppose there is a 6-month European put option with a strike price of 11. Answer the following questions (show all the details of your calculations and present your results with four decimal places) a) Draw a two-period binomial tree for the underlying asset. b) Calculate the price of the option today. c) Work forward on the tree and show that there is a self-financing trading strategy that replicates the value of the European put option at each node in the tree. d) Suppose the option is American. Calculate its price today