3. Consider a single period security market consisting of one bank account with interest rate r = 1 and a stock. Let the probability space be 12 = {wi, we} and S(0) = 5, S(1,wi) = 3, S(1,w2) = (i) Are there any arbitrage opportunities? If so, find them. If none, find all the risk neutral probability measures. [10 Marks] (ii) Is this model complete? (10 Marks] (iii) Consider a European call option in this model with exercise (i.e., strike) price K = 5. Calculate the price of this option and find its hedging portfolio. Then describe the hedging portfolio in your own words. [10 Marks) (iv) Consider a European put option in this model with exercise (i.e., strike) price K = 5. Calculate the price of this option and find its hedging portfolio. Then describe the hedging portfolio in your own words. [10 Marks] 3. Consider a single period security market consisting of one bank account with interest rate r = 1 and a stock. Let the probability space be 12 = {wi, we} and S(0) = 5, S(1,wi) = 3, S(1,w2) = (i) Are there any arbitrage opportunities? If so, find them. If none, find all the risk neutral probability measures. [10 Marks] (ii) Is this model complete? (10 Marks] (iii) Consider a European call option in this model with exercise (i.e., strike) price K = 5. Calculate the price of this option and find its hedging portfolio. Then describe the hedging portfolio in your own words. [10 Marks) (iv) Consider a European put option in this model with exercise (i.e., strike) price K = 5. Calculate the price of this option and find its hedging portfolio. Then describe the hedging portfolio in your own words. [10 Marks]