(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

2

$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 dier from the actual (1/2, 1/2) prob

ability. (c) (5 points) Derive the price of a security whose payo next year equals S1, where S1 is the

payo of one share of XYZ stock next year.

(d) (5 points). What is the expected return of XYZ stock under the "risk-neutral" probability mea

sure? Is this expected return dierent from the "true" expected return of stock XYZ? Explain why