Problem 1. Consider a stock S in a binary two-period model with value 100 USD at time t = 0. We assume that the value in each node increases by 27.5 percent in the up-state and decreases with 10 percent in the down-state. The risk free interest rate r = 5 percent.

1. (i) Calculate the risk neutral probability distribution at maturity T = 2.

2. (ii) A European put option gives the owner the right to sell the stock at maturity at the strike price K. Calculate the value of such a put option in each of the states at maturiy.

3. (iii) Calculate the arbitrage-free price p of a European put option written on the stock S with strike price K = 111 USD.