FRM Exam Part I · Credit Risk Transfer Mechanisms

Credit Default Swaps (CDS) Explained for FRM Part I

Updated 11 October 2026 · Fact-checked

A credit default swap is a contract where the protection buyer pays a periodic premium (the CDS spread) and the protection seller pays the loss, 1 − recovery rate times notional, if a credit event hits a reference entity. To solve questions, identify who pays what, then apply payout = notional × (1 − R) and premium = spread × notional × accrual.

Understand Credit Default Swaps (CDS)

A credit default swap (CDS) transfers the credit risk of a reference entity (a company or sovereign) from one party to another. The protection buyer pays a regular fee. The protection seller promises to compensate the buyer if a credit event occurs. It works like insurance, but you do not need to own the underlying bond.

The contract has two legs. The premium leg is the buyer's stream of payments, equal to the CDS spread (quoted in basis points per year) times the notional, usually paid quarterly. The protection leg is the seller's contingent payment, equal to notional × (1 − recovery rate), made only if a credit event happens before maturity. If the entity defaults between payment dates, the buyer typically pays the accrued premium up to the event date, and payments then stop.

Credit events are defined in ISDA documentation. The common ones are bankruptcy, failure to pay, and restructuring. Sovereign CDS also include repudiation or moratorium. Which events apply depends on the contract terms and the standard contract for the region and entity type, so read the question for the stated terms. An ISDA Determinations Committee decides whether an event has occurred.

There are two settlement methods. With physical settlement, the buyer delivers a defaulted bond (or deliverable obligation) with face value equal to the notional and receives par (100% of notional). With cash settlement, an auction sets the final price of the cheapest-to-deliver type of obligation, and the seller pays notional × (1 − final price/100). The recovery rate R equals the auction price as a fraction. Because the buyer can deliver any eligible obligation, the cheapest-to-deliver option has value to the buyer.

The CDS spread reflects default risk. A useful approximation is spread ≈ hazard rate × (1 − R), that is, the annual default probability times loss given default. A higher spread means higher perceived default risk or lower expected recovery. CDS spreads and bond spreads over the risk-free rate are usually close, but the difference (the CDS-bond basis) can be non-zero because of liquidity, funding and delivery options.

Key formulas to remember

Protection leg payout: Payout = Notional × (1 − R); R is the recovery rate (or final auction price as a fraction). Paid only on a credit event.
Annual premium: Annual premium = CDS spread × Notional; Spread in decimals: 120 bp = 0.0120. Quarterly payment ≈ annual premium ÷ 4 (actual/360 conventions may adjust slightly).
Spread approximation (credit triangle): s ≈ λ × (1 − R); λ is the annual hazard rate (default intensity). Approximation; assumes a flat hazard rate.
Implied hazard rate: λ ≈ s ÷ (1 − R); Rearranged form. Used to back out default probability from a quoted spread.
Approximate default probability: P(default within T years) ≈ 1 − e^(−λT); Use with constant hazard rate. Survival probability = e^(−λT).
Accrued premium on default: Accrual = Spread × Notional × (days since last payment ÷ 360); Check the day count in the question; the convention is typically actual/360.
Physical settlement: Buyer delivers bonds with face = Notional and receives Notional; Buyer's net loss recovered = Notional − market value of delivered bond.

How to solve Credit Default Swaps (CDS) questions

Use this sequence for almost any CDS question, whether it asks for a payment, a spread, a default probability or a settlement amount.

1Identify the roles: who is the protection buyer and who is the seller, and what is the reference entity and notional.
2Convert the spread from basis points to a decimal (1 bp = 0.0001) and note the payment frequency and day count.
3Decide if a credit event occurred and when. Premiums are paid up to the event date, including any accrued amount.
4Find the recovery rate R or the auction price. If given the price, R = price ÷ 100.
5Compute the protection payout as Notional × (1 − R), or for physical settlement, par for the delivered bond.
6Compute net cash flows for the party asked about: payout received minus premiums and accrual paid, or the reverse for the seller.
7For spread questions, use s ≈ λ(1 − R) and rearrange for the unknown, then convert to probability with 1 − e^(−λT) if needed.
8Check the sign and the units, and that your answer is for the party the question names.

Quickest way: Credit triangle shortcut

When to use it: Use when the question gives two of spread, hazard rate (or default probability) and recovery rate and asks for the third, or asks for a settlement amount.

Write s = λ(1 − R) and plug in the two known values in decimals.
Solve for the unknown. For a probability over T years, compute 1 − e^(−λT); for small λT, the answer is close to λT.
For payouts, multiply Notional by (1 − R) at once and ignore the premium leg unless asked for net cash flow.
Eliminate options with wrong units (basis points vs percent), then match to the remaining choice.

Common mistakes in Credit Default Swaps (CDS)

Paying out the full notional instead of notional × (1 − R).
Students confuse physical settlement, where par is paid against the bond, with the seller's net loss.
Fix: Ask what the seller truly loses: par paid minus the value of the bond received. That equals notional × (1 − R).
Treating a spread in basis points as a percentage.
A quote such as 150 gets used as 1.5 or 150%.
Fix: Divide basis points by 10,000 every time. 150 bp = 0.0150.
Forgetting accrued premium when default falls between payment dates.
Students assume premiums stop on the last payment date.
Fix: Add the accrual from the last payment date to the credit event date, paid by the buyer.
Mixing up who pays on a credit event.
The seller sounds like the insured party because it 'sells' the swap.
Fix: The buyer buys protection and pays the premium. The seller receives the premium and pays on default.
Using the credit triangle as an exact result.
It is a clean formula, so it feels exact.
Fix: Remember it assumes a constant hazard rate and ignores discounting and accrual. Use it only as an approximation unless told otherwise.
Assuming the buyer must own the reference bond.
The insurance analogy implies an insurable interest.
Fix: CDS can be bought without holding the bond (naked protection). Only physical delivery requires obtaining a deliverable obligation.

Worked examples

Example 1

A fund buys 5-year CDS protection on a corporate with notional $10,000,000 at a spread of 180 bp. The firm defaults. The auction sets the final price at 35% of par. Ignore accrued premium. What does the protection seller pay under cash settlement?

Show the solution

Notional = $10,000,000.
Recovery rate R = 35% = 0.35.
Payout = Notional × (1 − R) = 10,000,000 × 0.65.
Payout = $6,500,000.

Answer: $6,500,000

Example 2

A 5-year CDS on a bank trades at a spread of 240 bp. Assume a recovery rate of 40% and a constant hazard rate. Using the credit triangle, what is the approximate annual hazard rate, and the approximate probability of default within 5 years? Use e^(−0.20) = 0.8187.

Show the solution

Convert the spread: s = 240 bp = 0.0240.
Loss given default = 1 − R = 0.60.
Hazard rate λ ≈ s ÷ (1 − R) = 0.0240 ÷ 0.60 = 0.04, or 4% per year.
Survival probability over 5 years = e^(−λT) = e^(−0.04 × 5) = e^(−0.20) = 0.8187.
Default probability = 1 − 0.8187 = 0.1813, about 18.1%.

Answer: Hazard rate ≈ 4% per year; 5-year default probability ≈ 18.1%

Exam tips

Always convert basis points to decimals before any calculation, and state which party the question asks about.
Memorise the pair: payout = notional × (1 − R), and s ≈ λ(1 − R). Most numeric CDS questions reduce to one of them.
For settlement questions, remember that physical and cash settlement should give the seller the same economic loss, notional × (1 − R), if the delivered bond is worth R × par.
Know the credit event list: bankruptcy, failure to pay, restructuring, and for sovereigns repudiation or moratorium. Conceptual questions often test which event is included or excluded.
Expect conceptual items on the cheapest-to-deliver option and why CDS spreads and bond spreads can differ.

Practice questions from Credit Risk Transfer Mechanisms

Credit Default Swaps (CDS) in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Credit Default Swaps (CDS): frequently asked questions

How does a credit default swap work?

The protection buyer pays a periodic premium based on the CDS spread. If the reference entity suffers a credit event, the seller pays the buyer the loss, notional × (1 − recovery rate). If no event occurs, the buyer simply pays premiums until maturity.

What is the difference between physical and cash settlement of a CDS?

In physical settlement the buyer delivers a defaulted bond with face value equal to the notional and receives par. In cash settlement the seller pays notional × (1 − final auction price) and no bond changes hands. Both give the same economic result if the bond's value equals the auction price.

What are the credit events in a CDS under ISDA documentation?

Typical credit events are bankruptcy, failure to pay and restructuring. Sovereign contracts also include repudiation or moratorium. Which events apply depends on the contract terms, and an ISDA Determinations Committee rules on whether an event has occurred.

How do I calculate a CDS spread from default probability?

Use the credit triangle: spread ≈ annual hazard rate × (1 − recovery rate). For a 3% hazard rate and 40% recovery, spread ≈ 0.03 × 0.60 = 0.018, or 180 bp. It is an approximation that assumes a constant hazard rate.