4. (15 points) A stock price is currently $40. Over each of the next two three-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 12% per annum with continuous compounding. (1) What is the value of a six-month European put option with a strike price of $42? (2) What is the value of a six-month American put option with a strike price of $42? (3) Which option has a higher value? The European put option or the American put option