PROBLEM 1. (25 Points) Assume that the price S of a risky asset follows a binomial model with S(0) $100, u = market, the risk-free rate is 0% (zero). The time horizon will be N 10% and d -10%. The asset pays a dividend of $5 on the odd times, i.e., 1, 3,5... . In this 3 and the face value B(3,3) of the bond is 100. (a) (6 Points) Determine the ex-dividend stock price tree. Hint: It may be helpful to also include the "cum dividend" prices (b) (11 Points) Price and hedge a European call with strike price K = 87 and expiry date N = 3 (c) (11 Points) Price and hedge a European put with strike price K = 87 and expiry date N = 3. (d) (3 Points) Verify that the Put-Call Parity holds. Remark: In Parts (b) and (c) present only your results on a table whose columns are labeled "Node", "Position in shares", "Position in bonds", "Price of the option" PROBLEM 1. (25 Points) Assume that the price S of a risky asset follows a binomial model with S(0) $100, u = market, the risk-free rate is 0% (zero). The time horizon will be N 10% and d -10%. The asset pays a dividend of $5 on the odd times, i.e., 1, 3,5... . In this 3 and the face value B(3,3) of the bond is 100. (a) (6 Points) Determine the ex-dividend stock price tree. Hint: It may be helpful to also include the "cum dividend" prices (b) (11 Points) Price and hedge a European call with strike price K = 87 and expiry date N = 3 (c) (11 Points) Price and hedge a European put with strike price K = 87 and expiry date N = 3. (d) (3 Points) Verify that the Put-Call Parity holds. Remark: In Parts (b) and (c) present only your results on a table whose columns are labeled "Node", "Position in shares", "Position in bonds", "Price of the option