Question 1 (a) A bank offers a three-year bond with par value $1,000 with 8% coupon rates, semi- annually. The yield rate of this bond is 10% p.a. convertible semi-annually. What is the Macaulay duration of the three-year bond? [6 marks] (b) Suppose that the current stock price is $120 and the force of interest is 5% p.a. The stock price will either go up by 10% or down by 20% in one year. There is one American put option with exercise price of $125 that will expire in two years. What is the price of American put option? [8 marks] (c) An investor wants to exactly replicate the call option's payoff so he considers to buy X shares of the stock and Y shares of bonds. Suppose that the stock price is $80 and the bond price with coupon rate 4% is $100. The stock price will either go up 13% or down 12% in one year. There are one European call option and one European put option with exercise price of $75 that will expire in one year. Short selling is allowed. Let the price of the European Call option be $Z. What are the values of X, Y and Z? [6 marks]