1. Suppose you are a bond dealer looking for arbitrage opportunities. The first column in the table below shows the current prices of the four government bonds (without default risk). Assume that you can buy and short these bonds at a given price. The remaining columns of the table are the cash flows generated by the bonds at the end of the first, second and third years. All bonds mature at the end of the third year. Table 2-1 Bond The spot price CF(1 year) CF(2nd year) CF(3rd year) A 99.5 103 102.0 5 105 96.0 100 109 8 108 3 0 B 5 0 0 D 8 Are there arbitrage opportunities for the prices of these four types of bonds? If it exists, how can you seize this opportunity? 2. Consider a corporate bond with a coupon rate of 5%, a maturity of 4 years, and an interest payment every six months. The price is 97.50. The spot interest rate is as follows: Table 2-2 Period Years Spot Rate 1 0.5 2.2 2 1 2.5 3 1.5 3 4 2 3.25 5 2.5 3.5 3 3.85 3.5 4.05 8 4 4.3 6 7 Question: What is the nominal spread and Z-spread of the corporate bond? 3. According to the one-year interest rate tree given below with a period of one year, 2.75% is the current one-year interest rate. Calculate the value of a callable bond with the coupon rate of 5%, and it pay interest once a year with a 2-year maturity, whose redemption price is 103 after one year. (With 50% probability for each scenario) 3.25% 2.75% 2.90%