Credit default swaps

What is a credit derivative?

A credit derivative is based on the default risk of one borrower, or of a group of borrowers in an index. It lets an investor manage the risk of loss from default separately from owning the bond. The most common one is the credit default swap (CDS) .

CDS contracts trade on a spread, the CDS credit spread , much like the credit spread on a cash bond. That spread depends on the probability of default and on the loss given default. A higher spread means a higher chance of trouble, and a lower bond price. A lower spread means the reverse.

How does a CDS work?

In a CDS, the protection buyer pays the protection seller to take on the risk of loss if a third party, the reference entity, defaults. The reference entity can be a company, a sovereign, an index of issuers or a special purpose entity holding loans, mortgages or bonds.

• The buyer pays the CDS spread, a fixed annual rate on the notional, usually quarterly.
• The seller pays only if a credit event occurs.
• After a credit event the seller pays the buyer the loss given default (LGD) on the notional, and the contract ends.

Credit eventtriggers the seller's payment and ends the contract

• Bankruptcy Memorize
• Failure to pay Memorize a missed payment on an obligation
• Involuntary restructuring Memorize terms of the debt forced to change

The notional is never exchanged. It sets the size of the spread payments and of the payout.

$$\text{Payment} = N \times \dfrac{s}{10{,}000} \times \dfrac{1}{m}$$

Here s is the spread in basis points a year and m the number of payments a year.

$$L = N \times \text{LGD} = N \times (1 - RR)$$

RR is the recovery rate, the share of the exposure the lender gets back. LGD is what is lost: 1 − RR.

Who is long and who is short credit risk?

The seller receives a fixed spread and may have to pay out an uncertain amount at an uncertain time. That is similar to owning the borrower’s bond: the coupon includes a credit spread in return for a possible loss. The seller is therefore long credit risk.

The buyer is the opposite. A buyer who owns the borrower’s debt uses the CDS like insurance: if the debt loses value in a credit event, the payment from the seller offsets it. A buyer who owns no such debt gains when credit worsens and spreads widen, so the buyer is short credit risk.

Credit default swaptransfers the loss from a borrower's default; the notional is not exchanged

• Protection buyer Memorize pays the CDS spread; short credit risk
  • Hedger Use it holds the debt; the CDS offsets the loss, like insurance
  • Speculator Use it owns no debt; gains if credit spreads widen
• Protection seller Memorize receives the spread; long credit risk
  • Credit investor Use it earns the spread for taking the loss risk, like holding the bond

Party	Position	Typical motive
Bank holding a loan, buys protection	hedged (like insurance)	offset the loss if the borrower defaults
Fund buys protection without owning bonds	short credit risk	profit if spreads widen
Insurer sells protection	long credit risk	earn the spread, like holding the bond

Exam tip Credit risk is “the risk of loss from default”. Whoever loses when the borrower fails is long credit risk, and the bondholder and the protection seller both lose.

What happens to a CDS when credit quality changes?

The spread is fixed at the start. When the market spread for the same borrower widens, the buyer is paying less than the market charge and has a gain, while the seller has a loss. When the spread narrows, the reverse holds. The change in value is roughly the spread change times the notional times the effective duration of the remaining contract, in the same way as for any fixed-income instrument.

$$\Delta V \approx \Delta s \times N \times \text{EffDur}_{CDS}$$

A downgrade moves the spread and so the value of the contract, but it triggers no payment. Only a credit event ends the contract and creates the payout.

Why is a CDS called a swap if it is a contingent claim?

It shares features with both families. Like a swap, it involves periodic payments, the notional is not exchanged and a CDS agreed at the par spread has zero value at the start. Like an option, the seller’s payment is contingent: both its timing and its size depend on what the issuer does. Strictly, it is a contingent claim that shares some features of a firm commitment.

Go deeper Index CDS

An index CDS covers a basket of issuers, such as a high-yield credit index. Investors use it to change their exposure to a whole segment of the credit market quickly, without trading dozens of bonds. A credit event at one issuer settles that issuer’s share of the index and the rest of the contract continues.

Go deeper What drives the spread

The CDS spread reflects the probability of default and the loss given default, the same two drivers as the credit spread on a bond. The fixed income modules on credit risk build on this, and a CDS gives a direct market price for it.

Go deeper Settlement after a credit event

A CDS can settle in cash, where the seller pays the loss, or physically, where the buyer delivers the defaulted debt and receives the full notional. Both give the buyer the same economic outcome: notional less recovery.