(10 marks) 4. a) Consider a two year credit default swap (CDS) written on a loan of a company. The CDS nominal is f100 million. The firm can default in each of the two years. If the firm defaults, it happens at the very end of a year. The recovery rate is 60% of the nominal and it is paid immediately after default. The hazard rate (i.e., the risk-neutral probability of default during a specific year, conditional on prior survival) in each of the two years is 5%. The risk free rate is 2% per year with continuous compounding. Calculate the CDS premium if it is paid at the end of a year? (15 marks) b) Consider a two year corporate bond with a principal of $1000. The bond pays a 10% coupon per annum (compounded annually). Assume that the firm which issues the bond can default in each year, and the default always happens in the middle of a year. The hazard rate (i.e. the probability of default during a specific year conditional on prior survival) is 10% in the first year and 15% in the second year. In case of default, the recovery rate is 40% of the par paid immediately upon default. The risk-free rate is 5% per annum compounded continuously. Calculate the current bond price. Show your workings. (15 marks) c) Give two examples of other financial instruments apart from a CDS, which allow an investor to hedge against the default risk of a bond. Explain how the hedge works. (10 marks)Question 4 continued d) Consider the following bonds: (1) an ordinary 5 year bond with the coupon rate 10%, (2) a callable bond with the similar terms callable in years 3 and 4, (3) a similar callable bond callable any time from today, (4) a puttable bond with similar terms puttable in years 2 and 3. Rank these bonds in terms of their prices from the most expensive to the cheapest one. Explain briefly your answer. (10 marks)