For all questions, interest (r) and dividend () rates are continuously compounded unless specified otherwise.

For all of this question: r = 5%, = 1%, u = 1.07, d = 0.93

a) S₀ = $56, K = $50, T = 3 months. Find the price of the call option with strike K expiring at time T by finding the replicating portfolio and B.

b) S₀ = $45.70, K = $50, T = 3 months. Find the price of the call option with strike K expiring at time T by finding the replicating portfolio and B.

c) S₀ = $50, T = 3 months, C_up = the value of the call you got from part a), C_dn = the value of the call from part b). Price the call option at t = 0 using the replicating portfolio and B.

d) Draw the 2 step binomial tree for the stock prices using S₀ = $50, T = 6 months (so h = 3 months). See how you can combine parts a), b), and c) to price the call option with strike K expiring at time 6 months.

e) Compute the risk neutral probabilities p_up and p_dn and use those to price the same option. Do you get the same price as in d)?