1. (40 Points) Assume that the price S of a risky asset follows a binomial model with S(0) = $100, 10% and d = -10%. The asset pays a dividend of $5 on the odd times, i.e., 1,3,5.... In this market, the risk-free rate is 5% (zero). The time horizon will be N 3. U = = more (a) (3 Points) Determine the ex-dividend stock price tree. Hint: It may be helpful to also include the "cum dividend (b) (5 Points) Price a European call with strike price K 87 and expiry date N = 3 (calculate the value at every node). (c) (5 Points) Price a European put with strike price K = 87 and expiry date N 3 (calculate the value at every node). (d) (3 Points) Verify that the PutCall Parity holds. (e) (12 Points) Price an American call with strike price K = 87 and expiry date N = 3. (f) (12 Points) Price an American put with strike price K = 87 and expiry date N = 3. = = = = 1. (40 Points) Assume that the price S of a risky asset follows a binomial model with S(0) = $100, 10% and d = -10%. The asset pays a dividend of $5 on the odd times, i.e., 1,3,5.... In this market, the risk-free rate is 5% (zero). The time horizon will be N 3. U = = more (a) (3 Points) Determine the ex-dividend stock price tree. Hint: It may be helpful to also include the "cum dividend (b) (5 Points) Price a European call with strike price K 87 and expiry date N = 3 (calculate the value at every node). (c) (5 Points) Price a European put with strike price K = 87 and expiry date N 3 (calculate the value at every node). (d) (3 Points) Verify that the PutCall Parity holds. (e) (12 Points) Price an American call with strike price K = 87 and expiry date N = 3. (f) (12 Points) Price an American put with strike price K = 87 and expiry date N = 3. = = = =