a) A stock price is currently $100. Over each of the next two periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum. What is the value of a 1-year European call option with a strike price of $100? What would be the value if it was an American call option instead of European option?

b) A stock price is currently $80. It is known that at the end of year it will be either $75 or $85. The risk-free interest rate is 5% per annum. What is the value of a European put option with a strike price of $80? Also calculate the value in case of an American option.