A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 5% or down by 5%. The stock does not pay any dividend. The risk-free interest rate is 5% per annum with continuous compounding. 1) What is the value of a six-month European put option with a strike price of $51? 2) If the put option were American, would it ever he optimal to exercise it early at any of nodes on the tree? What would the value of this American put option be? 3) If the call option were American, would it ever be optimal to exercise it early? What would the value of this American call be? 4) What is the delta of the European put option described above at the initial node of a two-step tree