Consider a 3-month up-and-in European call barrier option. Consider a two-period binomial model for this option. The annual log return for the up-side stock price is u = 0.1 and the annual log return for the downside stock price is d = 0.05. This means that the stock price either becomes Sie u1.5/12 or Sie d1.5/12 after one period, for i = 0 or 1. The annual continuously compounding interest rate is r = 0.02. At the end of the second period, the payoff of this barrier option is V2 = (S2 K)+ if M2 B 0 otherwise , 1 where K is the strike price, B is the barrier level, and M2 = max0i2 Si . In other words, if M2 is larger than the barrier level B, the option is knocked in and the payoff at maturity is the standard European call; if M2 does not reach B, the option is worthless. Assume B = 101 and K = 100 for this problem. (a) (4 points) Draw a binomial tree model and write down stock prices on each node of the tree. Calculate the risk-neutral probabilities for this binomial tree model. (b) (8 points) Use the risk-neutral pricing method, find the risk-neutral price of this European call barrier option at time 0. (c) (10 points) If the seller of this option construct a replication strategy for this option, how many shares of stock the seller needs to buy/sell at time 0? Verify the replication strategy indeed replicates the barrier option payoff at the end of second period. (d) (3 points) If the barrier level B increases, will the option price for the European call barrier option increase or decrease? Please explain your reason.