Question

Suppose that the risk-free zero curve is flat at 6% per annum with continuous compounding and that defaults can occur at times 0.25 years, 0.75 years, 1.25 years, and 1.75 years in a two-year plain vanilla credit default swap with semi-annual payments. Suppose that the recovery rate is 20% and the unconditional probabilities of default (as seen at time zero) are 1% at times 0.25 years and 0.75 years, and 1.5% at times 1.25 years and 1.75 years.

i) Estimate the credit default swap (CDS) spread in the example above. ( 8 marks )

Answer 1

Sol :

PV of the expected regular payments (Payment rate = s per year) :

Time/Years	Survival probability	Expected payment (s)	Discount factor	PV of exp payment (s)
0.5	0.990	0.4950	0.9704	0.4804
1	0.980	0.4900	0.9418	0.4615
1.5	0.965	0.4825	0.9139	0.4410
2	0.950	0.4750	0.8869	0.4213
Total				1.8041

PV of expected payoffs (notional principal =$1) :

Time/Years	Probability of default	Recovery rate	Expected payoff	Discount factor	PV of expected payoff
0.25	0.010	0.2	0.008	0.9851	0.0079
0.75	0.010	0.2	0.008	0.9560	0.0076
1.25	0.015	0.2	0.012	0.9277	0.0111
1.75	0.015	0.2	0.012	0.9003	0.0108
Total					0.0375

PV of accrual payments :

Time/Years	Probability of default	Expected accural payment (s)	Discount factor	PV of expected accrual payment (s)
0.25	0.010	0.00250	0.9851	0.0025
0.75	0.010	0.00250	0.9560	0.0024
1.25	0.015	0.00375	0.9277	0.0035
1.75	0.015	0.00375	0.9003	0.0034
Total				0.0117

Therefore credit default swap (CDS) spread will be = 1.8041s + 0.0117s = 0.0375. CDS spread is 0.0206 or 206 basis points.