Core Path · L1.7.10

Credit default swaps

12 minDerivativesCredit risk

By the end you will be able to

  1. 1Explain how a CDS transfers default risk from the protection buyer to the protection seller.
  2. 2Calculate the premium payments and the payout after a credit event.
  3. 3Read a CDS spread as the market's price of default risk.
  4. 4Explain the counterparty risk in a CDS and why it matters most in a crisis.

Why it matters

A bank has lent €10 million to a car-parts maker and worries about the loan. It cannot easily sell the loan, and it does not want to upset its customer. Instead, it can pay someone else a yearly fee to take the default risk. That is a credit default swap.

Core explanation

Insurance against default, traded like a swap

A credit default swap (CDS) has two sides. The protection buyer pays a regular premium. The protection seller collects it and promises to cover the loss if a named borrower, the reference entity, defaults. The premium is quoted as a yearly spread in basis points of the notional and usually paid quarterly.

It works much like insurance on a bond, with two differences. You do not need to own the bond to buy protection, and the contract trades between financial firms like any other OTC derivative. A buyer with no bonds, a naked buyer, is simply betting that the borrower's credit will get worse.

What happens after a default

If a credit event happens, the seller pays the buyer the loss on the notional: notional × (1 − recovery). Most contracts are settled in cash, using a recovery rate fixed by an auction. If the auction prices the defaulted bonds at 40% of face value, the seller pays 60% of the notional. The premiums stop.

Step through the life of a credit event:

From missed payment to payout

1 / 5

Day 0

A payment is missed

The reference entity fails to pay a bond coupon. Most bonds allow a short grace period before this counts as a failure to pay.

Standard terms. Since 2009, most single-name CDS trade with standard terms: a fixed coupon (for example 100 or 500 basis points a year), paid on standard quarterly dates, with an upfront payment that makes up the difference between that coupon and the market spread. The idea is the same as here; the fixed coupons make contracts easier to net and clear.

A signal and a risk. CDS spreads are watched as a live price of default risk, often moving faster than credit ratings (L1.4.07). But a CDS carries a risk of its own: the seller must be able to pay. Defaults tend to arrive together in a crisis, just when sellers are weakest. L1.7.12 shows what happened when one huge seller could not pay.

The formal version

For notional NN, a spread ss (as a decimal, a year) and a recovery rate RR:

Premium each quarter=s×N4Payout after a credit event=N(1−R)\text{Premium each quarter} = \frac{s \times N}{4} \qquad \text{Payout after a credit event} = N(1 - R)

A rough link between the spread and the chance of default, often called the credit triangle, follows from making the expected premium equal the expected payout over one year:

s≈PD×(1−R)⟺PD≈s1−Rs \approx \text{PD} \times (1 - R) \qquad\Longleftrightarrow\qquad \text{PD} \approx \frac{s}{1 - R}

Here PD is the yearly chance of default the market is pricing. It is only a rule of thumb: it ignores discounting and the extra compensation sellers ask for bearing risk.

Try it

A 5-year CDS on €10m. Choose the spread, the recovery rate and the quarter of the credit event (slide to the end for no default). Watch how a small stream of premiums turns into one large payment.

Try itA CDS, quarter by quarter

Open the CDS model →
premium paid (37,500 a quarter) protection received (6,000,000)bars not to scale
Y1Y2Y3Y4Y5
Premiums paid337,500
Protection received6,000,000
Net to the buyer+5,662,500
Implied default chance a year2.50%

Rule of thumb: spread ÷ (1 − recovery).

Worked example

A bank protects a loan

A bank buys 5-year protection on a car-parts maker, notional €10,000,000, at 150 basis points a year, paid quarterly. Each quarter counts as a quarter of a year. Two years and a quarter in, just after its 9th premium, the company files for bankruptcy. The auction sets recovery at 40%.

Premiums and payout

Step 1 of 5
  1. 1

    The premium

    1.50% × €10,000,000 = €150,000 a year, or €37,500 a quarter.

Regulatory lens

Under the Basel framework, a bank that buys eligible CDS protection on a loan can reduce the capital it holds against it, by treating the exposure as if it were to the protection seller (L4.2). After 2008, standard index CDS between financial firms were made subject to central clearing in the US and the EU, and the EU's Short Selling Regulation banned naked CDS on EU government debt from November 2012.

Sparks

SparkWhen Greece triggered its CDS
In March 2012, Greece used new legal clauses to force all holders of its Greek-law bonds to accept a debt exchange with large losses. The ISDA Determinations Committee ruled that this was a credit event, and Greek government CDS paid out through an auction.
SparkInsurance you can buy on someone else's house
With most insurance, you must own what you insure. CDS has no such rule: you can buy protection on a company's debt without lending it anything. Critics compare this to insuring a neighbour's house; supporters say it makes the market for credit risk deeper and its prices more informative.

Key takeaways

  • In a CDS the buyer pays a regular premium and the seller pays the loss if the reference entity has a credit event.
  • Premium = spread × notional, usually paid quarterly. Payout = notional × (1 − recovery).
  • A Determinations Committee decides whether a credit event happened, and an auction fixes the recovery price.
  • The spread is a market price of default risk: roughly PD × (1 − R).
  • Protection is only as good as the seller, and sellers are weakest when defaults come together.

Reaction

Check what stuck

Question 1 · objective 1

In a credit default swap, who pays the regular premium?

Question 2 · objective 1

A CDS has a notional of USD 20m and a spread of 250 basis points a year, paid quarterly. Counting each quarter as a quarter of a year, how much is each quarterly payment, in dollars?

USD

Question 3 · objective 2

After a credit event, the auction fixes a recovery of 35%. How much does the seller pay on a CDS with notional USD 5m, in dollars?

USD

Question 4 · objective 3

A company's CDS trades at 300 basis points and the expected recovery rate is 40%. Using the rule of thumb, what yearly chance of default does the market imply, in %?

%

Question 5 · objective 4

A bank buys CDS protection on a company. Apart from that company, what is the main risk it still faces?

Glossary

Credit default swap
A contract in which one party pays a regular fee and the other pays out if a named borrower defaults.
Protection buyer
The side that pays the premium and is paid if a credit event happens. It is short the credit risk.
Protection seller
The side that receives the premium and pays out after a credit event. It takes on the credit risk.
Reference entity
The borrower whose default triggers the CDS, such as a company or a government.
CDS spread
The yearly premium, in basis points of the notional. 100 basis points = 1%.
Credit event
A default event defined in the contract: usually bankruptcy, failure to pay, and in some contracts restructuring.
Determinations Committee
An ISDA committee of dealers and investors that decides whether a credit event has happened.
Auction
A process run after a credit event to fix one market price for the defaulted bonds, used to settle all contracts.
Recovery rate
The share of face value a lender gets back after a default. Written R.
Naked CDS
Buying CDS protection without owning the bonds or loans of the reference entity.

Deep Dives & Origins

Deep Dives

  • John C. Hull, Options, Futures, and Other Derivatives, 11th edition (Pearson, 2021), the chapter “Credit Derivatives”. Intermediate.
  • Dominic O'Kane, Modelling Single-name and Multi-name Credit Derivatives (Wiley, 2008). Advanced.

Origins

  • John C. Hull, Options, Futures, and Other Derivatives, 11th edition, Pearson, 2021.
  • ISDA, 2014 ISDA Credit Derivatives Definitions.
  • Regulation (EU) No 236/2012 on short selling and certain aspects of credit default swaps.
  • Basel Committee on Banking Supervision, Basel Framework, CRE22 (credit risk mitigation).

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