(40 points) For a 1-year European put option on a stock, you are given: (a) The stock price is 41. (b) The strike price is 40 (c) 0.3 (d) The continuously compounded risk-free rate is 8% (e) There are no dividends f) The tree has 3 periods. (1) Price and hedge the European put option. (30 points) (2) Assume that the stock price turns out to goes down at time 1 (after 4 months) and the observed put option (8-month European put option on this stock with strike price 40) price is 2, construct an abitrage portfolio. (5 points) (3) Verify the European put price bounds at time 0. (5 points) (40 points) For a 1-year European put option on a stock, you are given: (a) The stock price is 41. (b) The strike price is 40 (c) 0.3 (d) The continuously compounded risk-free rate is 8% (e) There are no dividends f) The tree has 3 periods. (1) Price and hedge the European put option. (30 points) (2) Assume that the stock price turns out to goes down at time 1 (after 4 months) and the observed put option (8-month European put option on this stock with strike price 40) price is 2, construct an abitrage portfolio. (5 points) (3) Verify the European put price bounds at time 0. (5 points)