1) A stock price is currently $100. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100? 2) For the situation considered in the previous problem, what is the value of a one-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy putcall parity. 3) If the put option in the previous problem was American, would it ever be optimal to exercise it early at any of the nodes on the tree? Find the value of this American put option.

Please explain it step by step without using any excel.