Binomial Model:

(a) (10 points) Shares of XYZ stock cost $50 today and will sell for either $125 or $50 next year, with equal probability (1/2,1/2). A one-year zero coupon bond with face value $150 is selling for $100 today. What is the replicating portfolio and the price of a European put with strike equal to $72.5?

(b) (5 points) Derive the risk-neutral probability implied by the prices provided in the previous point. Clearly explain why the risk-neutral probability may differ from the actual (1/2, 1/2) probability.

(c) (5 points) Derive the price of a security whose payoff next year equals S1, where S1 is the payoff of one share of XYZ stock next year.

(d) (5 points). What is the expected return of XYZ stock under the risk-neutral probability measure? Is this expected return different from the true expected return of stock XYZ? Explain why.