The CDS curve in question is shown below in Figure 1: Quoted Flat CDS CDS Maturity (Years) Spread (bp) 1 30 2 40 50 60 70 80 90 100 110 10 120 The CDS spreads shown in this table are Quoted Flat Spreads assuming a fixed coupon of 100bps, they are NOT Par Spreads. In this coursework candidates will be required to calculate the risky annuity of various points of the CDS curve and under different assumptions. This coursework assumes an annual convention for the calculation of the risky annuity, such that: Risky Annuity = - PS PS 1+r (1+r) ++ PSt (1+r) where t is the maturity (in years) of the CDS, is the risk free rate and PS, is the cumulative survival probability over / years. The Hazard Rate using Flat Spread convention is assumed to be constant when calculating the risky annuity for a specific point in the CDS curve; this is not the case for a par spread curve. The risk free rate is constant and equal to 1% and the CDS curve recovery rate is 40%. Question 1. a) For each maturity of the Flat CDS curve, calculate: Average annual default probability over -years (assuming Flat Spread convention). Two decimal places, % number (xx%). Risky Annuity for the -years CDS (assuming Flat Spread convention). Three decimal places (.xxx). CDS upfront that would be payable by the buyer of protection to enter a 100bps fixed coupon CDS trade. Three decimal places in % of notional (.xxx%). b) Calculate the risky duration for each point on the CDS curve; i.e. the change in upfront that would result from a 1bp increase in the quoted spread. c) Is there a CDS for which Risky Annuity and Risky Duration are very similar? Why? Table 1: CDS Curve 600 W N 3 4 5 6 7 8 9 The CDS curve in question is shown below in Figure 1: Quoted Flat CDS CDS Maturity (Years) Spread (bp) 1 30 2 40 50 60 70 80 90 100 110 10 120 The CDS spreads shown in this table are Quoted Flat Spreads assuming a fixed coupon of 100bps, they are NOT Par Spreads. In this coursework candidates will be required to calculate the risky annuity of various points of the CDS curve and under different assumptions. This coursework assumes an annual convention for the calculation of the risky annuity, such that: Risky Annuity = - PS PS 1+r (1+r) ++ PSt (1+r) where t is the maturity (in years) of the CDS, is the risk free rate and PS, is the cumulative survival probability over / years. The Hazard Rate using Flat Spread convention is assumed to be constant when calculating the risky annuity for a specific point in the CDS curve; this is not the case for a par spread curve. The risk free rate is constant and equal to 1% and the CDS curve recovery rate is 40%. Question 1. a) For each maturity of the Flat CDS curve, calculate: Average annual default probability over -years (assuming Flat Spread convention). Two decimal places, % number (xx%). Risky Annuity for the -years CDS (assuming Flat Spread convention). Three decimal places (.xxx). CDS upfront that would be payable by the buyer of protection to enter a 100bps fixed coupon CDS trade. Three decimal places in % of notional (.xxx%). b) Calculate the risky duration for each point on the CDS curve; i.e. the change in upfront that would result from a 1bp increase in the quoted spread. c) Is there a CDS for which Risky Annuity and Risky Duration are very similar? Why? Table 1: CDS Curve 600 W N 3 4 5 6 7 8 9
