II. (10 points) A stock price is currently 100 . Over each of the following two six-month periods, it is expected to go up by 30% or down by 30%. The risk-free interest rate is 5% per annum with continuous compounding. An American put option on the stock will expire in one year, with a strike price of $88. a) Will it be optimal for an option holder to exercise her option early (i.e., 6 months from now)? (5 points) b) What is the price of the put option? (5 points) V. (15 points) Consider the same setup as in question III. Now assume that the central bank announced that six-month from now the risk-free rate will decrease from 5% per annum to 0% per annum. Also assume that the stock price movements are not impacted by this announcement. a) Will it be optimal for an option holder to exercise her option early (i.e., 6 months from now)? (6 points) b) Find the price of the American put option. (6 points) c) Without calculation, do you think an identical European put option is worth the same, more, or less than the price in part b)? Explain briefly ( 3 points) II. (10 points) A stock price is currently 100 . Over each of the following two six-month periods, it is expected to go up by 30% or down by 30%. The risk-free interest rate is 5% per annum with continuous compounding. An American put option on the stock will expire in one year, with a strike price of $88. a) Will it be optimal for an option holder to exercise her option early (i.e., 6 months from now)? (5 points) b) What is the price of the put option? (5 points) V. (15 points) Consider the same setup as in question III. Now assume that the central bank announced that six-month from now the risk-free rate will decrease from 5% per annum to 0% per annum. Also assume that the stock price movements are not impacted by this announcement. a) Will it be optimal for an option holder to exercise her option early (i.e., 6 months from now)? (6 points) b) Find the price of the American put option. (6 points) c) Without calculation, do you think an identical European put option is worth the same, more, or less than the price in part b)? Explain briefly ( 3 points)