State what a credit default swap (CDS) is and set out how it works, including what each of the protection buyer and the protection seller must do.
The idea
A credit default swap is a contract that insures the buyer against default by a reference entity. The protection buyer pays a periodic premium until maturity or a credit event. The premium is the CDS spread, quoted in basis points per year of the notional and usually paid quarterly. Let N be the notional and R the recovery rate of the reference obligation. If a credit event occurs, the protection seller pays the buyer the notional less the recovery value, so the payout is: Payout = N × (1 − R). Settlement is either physical or in cash. In physical settlement the buyer delivers bonds with face value equal to the notional and receives par. In cash settlement the seller pays the difference between par and a post-default market price, usually set by an auction. The buyer also pays the premium accrued since the last payment date. Because the buyer chooses which deliverable bond to hand over, there is a cheapest-to-deliver option. Neither party needs to own the bond.
Formulas
CDS payment on a credit event
CDS payment = notional × (1 − R)
- notional
- the notional amount of protection
- R
- the recovery rate, as a share of face value
Cash settlement uses the post-default price, usually from an auction, as R. Paying N × R is the slip; the buyer also owes accrued premium.
A practice question
Which statement correctly describes a credit default swap?
- The protection seller pays a periodic premium and receives a payment from the buyer if the reference entity defaults.Why not: Reverses the direction of the cash flows.
- The protection buyer must own the reference bond, and the contract pays only if that bond is sold at a loss.Why not: Ownership of the bond is not required, and payment depends on a credit event, not a sale.
- The protection buyer pays a periodic premium and receives a payment from the seller if the reference entity suffers a credit event. - correct
- The two parties exchange fixed and floating interest payments, with default simply ending the swap.Why not: Describes an interest rate swap; a CDS pays out on default.
A CDS is credit insurance: premium in, contingent payment out for the buyer, and the buyer need not hold the underlying bond.
A harder one
A bank bought 5-year protection on USD 50 million of a corporate loan at a CDS spread of 130 basis points. One year later the 4-year CDS spread on the same name has widened to 220 basis points. Taking the risk-adjusted annuity factor for four years as 3.70, the mark-to-market on the bank's CDS position is closest to:
- a loss of USD 1.66 millionWhy not: Gets the sign wrong; the protection buyer gains when spreads widen.
- a gain of USD 1.66 million - correct
- a gain of USD 1.80 millionWhy not: Multiplies by four years of undiscounted payments instead of the risk-adjusted annuity factor.
- a gain of USD 0.45 millionWhy not: Counts only one year of the spread difference.
MTM = (220 - 130 bp) x 50 million x 3.70 = 0.009 x 50,000,000 x 3.70 = USD 1.66 million gain, because the buyer locked in a cheap premium.
The hardest tier
A protection buyer holds a CDS on USD 25 million notional with a spread of 200 basis points paid quarterly. A credit event occurs two months after the last premium date, and the reference bond is later valued at 30 per 100 of face value. Under cash settlement, the net amount the buyer receives is closest to:
- USD 17,583,333Why not: Adds the accrued premium to the payout; the buyer owes the accrual, so it is deducted.
- USD 17,375,000Why not: Deducts a full quarter of premium instead of two months of accrual.
- USD 17,416,667 - correct
- USD 17,500,000Why not: Ignores the accrued premium that the buyer owes up to the credit event.
Payout = 25m x 0.70 = USD 17,500,000. Accrued premium = 25m x 2% x 2/12 = USD 83,333, which the buyer pays. Net = USD 17,416,667.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
Start free →More in Estimating Default Probabilities
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