Problem #9: Consider an American put option on a stock, with a $66 strike and 1-year to expiration. The stock has a [9 marks] continuous dividend yield of 6%, and its current price is $22. Suppose the volatility of the stock is 29%. The continuously compounded risk-free interest rate is 3%. Use a three-period lognormal tree to calculate the following: (a) The payoff at time 2: Up movement. (b) The payoff at time 2: Middle movement. (C) The payoff at time 2: Down movement. (d) The payoff at time 1: Up movement. (C) The payoff at time 1: Down movement. (1) The option cost at time 0. Problem #9: Consider an American put option on a stock, with a $66 strike and 1-year to expiration. The stock has a [9 marks] continuous dividend yield of 6%, and its current price is $22. Suppose the volatility of the stock is 29%. The continuously compounded risk-free interest rate is 3%. Use a three-period lognormal tree to calculate the following: (a) The payoff at time 2: Up movement. (b) The payoff at time 2: Middle movement. (C) The payoff at time 2: Down movement. (d) The payoff at time 1: Up movement. (C) The payoff at time 1: Down movement. (1) The option cost at time 0