2. The possible stock prices for XYZ Corporation over the next two years are:

Year: 0 1 2

S_uu = 70

P_uu=

S_u = 60

P_u=

S =50 S_ud = 50

P = P_ud =

S_d = 40

P_d=

S_dd = 30

P_dd=

The risk-free interest rate is 10% per year and the stock pays no dividends. Consider a European put with an exercise price of $44 and a time to expiration of 2 years.

a). Compute the risk-neutral probabilities for the stock price to go up at year 0 and year 1 (Note: the probability might be different for each node).

b). What is the risk-neutral probability for the put to expire in the money?

c). Compute the value of the put at year 0 using the risk-neutral pricing approach.

d). Solve for the replication portfolio for the put at year 0.

e). How should the replication portfolio be adjusted at the up node in year 1? What is the adjustment cost?

f). Consider a two-year American put with the same strike. Compute the early exercise premium of the American put.