PROBLEM 2. (25 Points) Assume that the price S of a risky asset follows a binomial model with u = 10%, d = -10%. In this market, the risk-free rate is 5%. The time horizon will be N = 3 and the face value B(3,3) of the bond is 100. (a) (3 Points) Determine the tree corresponding to the stock prices. (b) (8 Points) Determine the tree corresponding to the prices of an American put option with strike price X = 50 and expiry date N = 3. Moreover, determine when it is optimal for the holder of the option to exercise. (c) (9 Points) Hedge the aforementioned option. (Present your results in a table as in Problem 1 where the last column determines the required capital.) (d) (5 Points) Assume that you are the writer of the option and that the holder decides to exercise at the node (2, 2). Do you expect to have any (strictly positive) profit? If yes, determine it and explain why this is not an outcome of an arbitrage opportunity. PROBLEM 2. (25 Points) Assume that the price S of a risky asset follows a binomial model with u = 10%, d = -10%. In this market, the risk-free rate is 5%. The time horizon will be N = 3 and the face value B(3,3) of the bond is 100. (a) (3 Points) Determine the tree corresponding to the stock prices. (b) (8 Points) Determine the tree corresponding to the prices of an American put option with strike price X = 50 and expiry date N = 3. Moreover, determine when it is optimal for the holder of the option to exercise. (c) (9 Points) Hedge the aforementioned option. (Present your results in a table as in Problem 1 where the last column determines the required capital.) (d) (5 Points) Assume that you are the writer of the option and that the holder decides to exercise at the node (2, 2). Do you expect to have any (strictly positive) profit? If yes, determine it and explain why this is not an outcome of an arbitrage opportunity