PROBLEM 1. Assume that the price of a risky asset follows a binomial model with S(0) = $100, u = 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 0% (zero). The time horizon will be N = 3 and the face value B(3, 3) of the bond is 100. (a) (4 Points) Determine the ex-dividend stock price tree, Hint: It may be helpful to also include the "cum dividend" prices. (b) (10 Points) Price and hedge a European call with strike price K = 87 and expiry date N = 3. (c) (10 Points) Price and hedge a European put with strike price K = 87 and expiry date N = 3. (d) (5 Points) Verify that the Put-Call Parity holds. PROBLEM 1. Assume that the price of a risky asset follows a binomial model with S(0) = $100, u = 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 0% (zero). The time horizon will be N = 3 and the face value B(3, 3) of the bond is 100. (a) (4 Points) Determine the ex-dividend stock price tree, Hint: It may be helpful to also include the "cum dividend" prices. (b) (10 Points) Price and hedge a European call with strike price K = 87 and expiry date N = 3. (c) (10 Points) Price and hedge a European put with strike price K = 87 and expiry date N = 3. (d) (5 Points) Verify that the Put-Call Parity holds