CFA Level II Exam · Credit Default Swaps

CDS Pricing: Spreads, Upfront Premium and Hazard Rate

Q: How do I calculate the upfront premium on a CDS?

Subtract the standard coupon from the CDS spread, then multiply by the effective spread duration. For a 160 bps gap and duration of 4.5, the premium is 7.2% of notional. Multiply by notional for the cash amount.

Q: Why is CDS price roughly 100 minus the upfront premium?

CDS prices are quoted like bond prices per 100 of notional. Protection with a high spread has a large upfront premium, which shows up as a price below 100. It is an approximation.

Q: Is credit spread really PD times LGD?

It is an approximation for the expected annual loss. It ignores risk premiums and timing. Use it when the question asks for an approximate relationship.

Q: What is the difference between hazard rate and probability of default?

The hazard rate is the probability of default in a period given survival to the start of that period. The unconditional probability of default is the survival probability to that start multiplied by the hazard rate.

Updated 7 October 2026 · Fact-checked

CDS pricing converts a running credit spread into an upfront premium. Because the contract pays a fixed standard coupon, the buyer pays or receives the difference in value. Upfront premium ≈ (CDS spread − coupon) × duration. CDS price ≈ 100 − upfront premium %. Spread ≈ PD × LGD.

Understand CDS Pricing: Spreads, Upfront Premium and Hazard Rate

A credit default swap (CDS) is protection against default. The protection buyer pays a periodic premium. The protection seller pays out if a credit event happens. The payout equals the loss: notional × LGD.

The market quotes a CDS spread, the annual cost of protection that makes the contract fair. A rough link is: spread ≈ annual probability of default × loss given default. LGD = 1 − recovery rate. A high recovery rate means a lower LGD and so a lower spread for the same default probability.

Standardized contracts pay a fixed coupon, typically 100 bps for investment grade and 500 bps for high yield. The coupon rarely equals the fair spread. So a cash payment is made at inception to fix the gap. This is the upfront premium. If the spread is above the coupon, the buyer pays upfront. If the spread is below the coupon, the buyer receives it.

The hazard rate is the conditional probability of default in a period, given survival to that point. Survival over several years is the product of (1 − hazard) each year. The unconditional probability of default in a year is the survival probability to the start of the year × the hazard rate. Do not confuse the two.

The CDS price is quoted per 100 of notional, like a bond. Price ≈ 100 − upfront premium (in %). When the spread is wider than the coupon, the CDS price is below 100 and the protection buyer pays an upfront premium.

Key formulas to remember

Spread approximation: CDS spread ≈ PD × LGD; PD is the annual probability of default. It is an approximation, so use it when the question says so.
Loss given default: LGD = 1 − recovery rate; Recovery rate is a % of notional recovered after default.
Upfront premium (%): Upfront premium % ≈ (CDS spread − CDS coupon) × effective spread duration; Positive means the protection buyer pays. Negative means the buyer receives.
CDS price: CDS price ≈ 100 − upfront premium %; Quoted per 100 of notional.
Upfront payment: Upfront payment = upfront premium % × notional; Convert the % to a decimal first.
Survival probability: Survival to year n = (1 − h₁)(1 − h₂)…(1 − hₙ); h is the hazard rate, the conditional default probability each year.
Cumulative default probability: PD over n years = 1 − survival to year n; Use this for multi-year default probability.
Implied PD from spread: PD ≈ CDS spread ÷ LGD; Rearranged from the spread approximation.

How to solve CDS Pricing: Spreads, Upfront Premium and Hazard Rate questions

Read the vignette for the spread, coupon, duration, recovery rate and notional. Then pick the formula that links what you have to what is asked.

1List the data from the vignette: spread, standard coupon, duration, recovery, notional, hazard rates.
2Convert all basis points to decimals (100 bps = 0.01) and percentages to decimals.
3If asked for PD or spread, use spread ≈ PD × LGD with LGD = 1 − recovery.
4If asked for an upfront premium, compute (spread − coupon) × duration and note the sign.
5Apply the sign: positive means the buyer pays the seller. Negative means the buyer receives.
6For price, compute 100 − upfront premium in % terms.
7For multi-year default, multiply the yearly survival probabilities, then take 1 minus the product.
8Check the answer is sensible: wider spread than coupon means price below 100.

Quickest way: Spread-minus-coupon shortcut

When to use it: Any question giving a spread, a standard coupon and a duration, asking for upfront premium, price or the payer.

Subtract the coupon from the spread in bps.
Multiply by duration and divide by 10,000 to get a decimal. That is the upfront premium.
Price = 100 − (premium × 100).
Sign tells you who pays: spread above coupon, buyer pays.
For PD, divide spread by LGD.

Common mistakes in CDS Pricing: Spreads, Upfront Premium and Hazard Rate

Using the full spread instead of spread minus coupon for the upfront premium.
Students forget the contract already pays the coupon each period.
Fix: Only the gap between spread and coupon is settled upfront.
Using the recovery rate instead of LGD in spread = PD × LGD.
Both numbers appear in the vignette.
Fix: Always compute LGD = 1 − recovery first.
Getting the sign of the upfront payment wrong.
Students do not think about who is under-compensated.
Fix: If spread > coupon, the seller needs extra, so the buyer pays. If spread < coupon, the buyer receives.
Treating the hazard rate as the unconditional probability of default.
Both are called default probability.
Fix: Hazard is conditional on survival. Multiply by survival to the start of the year to get the unconditional figure.
Adding yearly hazard rates to get multi-year default probability.
It feels like cumulative addition.
Fix: Multiply (1 − h) terms for survival, then subtract from 1.
Forgetting to convert bps to decimals, giving upfront premiums 100 times too large.
Spreads are quoted in bps, prices in percent.
Fix: Write 250 bps as 0.0250 before multiplying.

Worked examples

Example 1

A 5-year CDS on Company X has a standard coupon of 100 bps and a quoted spread of 260 bps. The effective spread duration is 4.5. Notional is €10 million. (1) What is the upfront premium in %? (2) Who pays it and how much? (3) What is the approximate CDS price?

Show the solution

Spread minus coupon = 260 − 100 = 160 bps = 0.0160.
Upfront premium = 0.0160 × 4.5 = 0.072, or 7.2%.
Spread is above coupon, so the protection buyer pays the seller.
Upfront payment = 7.2% × €10,000,000 = €720,000.
Price ≈ 100 − 7.2 = 92.8.

Answer: (1) 7.2%. (2) The protection buyer pays €720,000. (3) About 92.8.

Example 2

Company Y has a recovery rate of 40%. Its 3-year CDS spread is 180 bps. Its yearly hazard rates are 2% in year 1, 3% in year 2 and 4% in year 3. (1) Approximate the annual PD implied by the spread. (2) What is the probability of surviving three years? (3) What is the unconditional probability of default in year 2?

Show the solution

LGD = 1 − 0.40 = 0.60.
PD ≈ spread ÷ LGD = 0.0180 ÷ 0.60 = 0.03, or 3.0%.
Survival year 1 = 0.98. Survival to end of year 2 = 0.98 × 0.97 = 0.9506.
Survival to end of year 3 = 0.9506 × 0.96 = 0.912576, about 91.26%.
Unconditional default in year 2 = survival to start of year 2 × hazard = 0.98 × 0.03 = 0.0294.

Answer: (1) About 3.0% per year. (2) About 91.26%. (3) 2.94%.

Exam tips

Write down who is buyer and seller before computing. Many answer options differ only by sign or direction.
Check whether the vignette gives duration. If not, the question likely wants the PD × LGD route.
Hazard rate wording signals the conditional versus unconditional trap. Reread the question's year.
Questions often ask for price. Do 100 minus premium in percent, not in decimal.
There is no penalty for wrong answers, so never leave a question blank.