Different options having the same stock as the underlying asset are traded on the market. Suppose that the risk-free interest rate is 4% per year, that the current stock price is 20 euros and that the price either goes up by 25% or down by 25% in each of the next 3 periods. Each period is 6 months. (a) Consider a European Call option with strike of 18 euros and maturity of 18 months. i. Draw a binomial tree for the stock and indicate its stock prices. You only need to write the stock prices inside the circles; you may skip II(t;X) if you prefer. ii. Compute II(0:X). iii. Construct a replicating portfolio ho = (10; Yo), and show that V" = 11(0; X). (b) Repeat Part (a) with the corresponding Put option with strike of 18 euros and with maturity of 18 months. Different options having the same stock as the underlying asset are traded on the market. Suppose that the risk-free interest rate is 4% per year, that the current stock price is 20 euros and that the price either goes up by 25% or down by 25% in each of the next 3 periods. Each period is 6 months. (a) Consider a European Call option with strike of 18 euros and maturity of 18 months. i. Draw a binomial tree for the stock and indicate its stock prices. You only need to write the stock prices inside the circles; you may skip II(t;X) if you prefer. ii. Compute II(0:X). iii. Construct a replicating portfolio ho = (10; Yo), and show that V" = 11(0; X). (b) Repeat Part (a) with the corresponding Put option with strike of 18 euros and with maturity of 18 months