Consider a three-period model with two assets stock and risk-free bankaccount.

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=3/4, pd=1/4. The risk-free rate of return, in each period, is constant and equal to r= 0.05. The initial stock price is1000.

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{MS3K,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 optionat 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 portfoliothat perfectly replicates the payoff of the look-back option