a) A stock price is currently $50. Over each of the next two periods of four months, it is expected to go up by 15% 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 put option with a strike price of $45 ? [15 marks] b) What is the answer if the one year put option is American instead of European? [10 marks]