Set up:

• Assume that the stock price for XYZ Corp follows a binomial lattice
• Assume the lattice has a multiplicative structure and
• the stock either moves up by multiple u=5/4 or down by a multiple d=1/u=4/5
• the stock moves up or down with equal probability
• let S₀=10 denote the initial value of the stock and S_n it's value after n-steps
• There is also a risk free asset available with r_f=0

(a) For a one-period model (i.e. S₀ -> S₁), find the state prices as well as the risk-neutral probabilities

(b) Compare the objective probabilities (i.e. 50% up or down) with the risk-neutral probabilities found in (a). Are they the same or different? Why?

(c) Draw the lattice for two periods

(d) Price a European put option with expiry n=2 and strike K=$8.40

(e) Find the replicating trading strategy that perfectly hedges this option

(Note: Trading strategy means portfolio holdings of the stock and the risk free asset at each node on the lattice in (c))