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 (t;X) if you prefer. ii. Compute (0;X). iii. Construct a replicating portfolio h0 = (x0; y0), and show that Vh0 = (0;X).

(b) Repeat Part (a) with the corresponding Put option with strike of 18 euros and with maturity of 18 months.