(i) Consider a non-dividend paying stock with current price $100 and return volatility = 18.23 [% p.a.]. Construct the one-period (T=1) binominal tree. The risk-free one-period rate y(0;1) is 3%. Value a European Call with exercise price E= $110 and maturity T = 1 by the replication principle, the hedging principle, and by means of risk-neutral probabilities (ii) Consider the stock price as defined in (i). Value a European Putn with exercise price E=110 using all three valuation methods of (i). (iii) Extend the one-period binominal tree of (i) to a two period (T=2) recombining tree. Assume y(0;2) = 3%. Value two year European and American Calls with exercise price E=110. (iv) Value two-year European and American Puts using the tree constructed in subproblem (iii). (v) Assume the stock pays in t=1 a 5% dividend on the stock price S1cum. Solve (iii) and (iv) for this case of a dividend paying stock. Compare the results of the European and American Call resp. and try to explain the differences. (vi) Solve (v) for the European and American Call if a dividend of 15% on the cum-stock price is paid.