Consider a three-period model with two assets stock and risk-free bank account. The one-period stock returns are independent and identically distributed, and each can take two values, Ru 1.2 or Rd = 0.9 with objective probabilities pu = i; pa = 1. The risk-free rate of return, in each period, is constant and equal to r = 0.05. The initial stock price is 1000. a. Construct the stock price tree. b. Calculate the risk-neutral probabilities in each one-period sub-model. c. Consider a look-back option with payoff max {MS3 K,0}, where K = 1000 is the strike price and MS3 = max {S0, S1, S2, S3}, with St the stock price in period t. Write the payoff of the look back option at the terminal nodes of the tree at t = 3. d. Price the look-back option recursively, using the risk-neutral proba- bilities obtained in part (b). e. At t = 0 find the amount deposited in (or borrowed from) the bank, and the number of shares required for the self-financing portfolio that perfectly replicates the payoff of the look-back option. Consider a three-period model with two assets stock and risk-free bank account. The one-period stock returns are independent and identically distributed, and each can take two values, Ru 1.2 or Rd = 0.9 with objective probabilities pu = i; pa = 1. The risk-free rate of return, in each period, is constant and equal to r = 0.05. The initial stock price is 1000. a. Construct the stock price tree. b. Calculate the risk-neutral probabilities in each one-period sub-model. c. Consider a look-back option with payoff max {MS3 K,0}, where K = 1000 is the strike price and MS3 = max {S0, S1, S2, S3}, with St the stock price in period t. Write the payoff of the look back option at the terminal nodes of the tree at t = 3. d. Price the look-back option recursively, using the risk-neutral proba- bilities obtained in part (b). e. At t = 0 find the amount deposited in (or borrowed from) the bank, and the number of shares required for the self-financing portfolio that perfectly replicates the payoff of the look-back option