3. Consider the following problem: Suppose that the probability of an entity defaulting during a year conditional on no earlier default is 2%. Assume that defaults always happen halfway through a year. The risk-free rate is 5% per annum with continuous compounding and the recovery rate is 40%. Assume that payments on a 3-year credit default swap (CDS) are made once a year, at the end of each year. The credit default spread is equal to s basis points. That is, payments are made at the rate of s per year and the notional principal is 1. The accrual payment of 0.5s made in the event of a default. (a) Calculate the survival probabilities and unconditional default probabilities for each of the three years. [20 marks] (b) Calculate the present value of the expected payments made on the CDS. [20 marks] (c) Calculate the present value of the expected payoff. [20 marks] (d) Calculate the present value of the expected accrual payments. [20 marks] (e) From the answer of (a) - (d), what is s equal to? Suppose the CDS had been negotiated some time ago for a spread of 200 basis points. Calculate the value of swap to the seller/buyer. [20 marks] 3. Consider the following problem: Suppose that the probability of an entity defaulting during a year conditional on no earlier default is 2%. Assume that defaults always happen halfway through a year. The risk-free rate is 5% per annum with continuous compounding and the recovery rate is 40%. Assume that payments on a 3-year credit default swap (CDS) are made once a year, at the end of each year. The credit default spread is equal to s basis points. That is, payments are made at the rate of s per year and the notional principal is 1. The accrual payment of 0.5s made in the event of a default. (a) Calculate the survival probabilities and unconditional default probabilities for each of the three years. [20 marks] (b) Calculate the present value of the expected payments made on the CDS. [20 marks] (c) Calculate the present value of the expected payoff. [20 marks] (d) Calculate the present value of the expected accrual payments. [20 marks] (e) From the answer of (a) - (d), what is s equal to? Suppose the CDS had been negotiated some time ago for a spread of 200 basis points. Calculate the value of swap to the seller/buyer. [20 marks]