CFA Level II Exam · Credit Default Swaps

CDS Valuation and Changes After Inception

Updated 7 October 2026 · Fact-checked

After inception, the change in a CDS's value is approximately the change in the market spread × risk duration × notional. A wider spread gains for the protection buyer and loses for the seller. Measured against the fixed coupon, the total value is (current spread − coupon) × duration. With an unchanged spread, value converges to zero as maturity nears.

Understand CDS Valuation and Changes After Inception

A CDS is priced at inception so that both sides see fair value. The protection buyer pays a fixed coupon (standardised at 100 or 500 bps for the contracts you will see). The coupon is usually not equal to the market spread, so an upfront payment makes up the difference. Once that upfront payment is counted, the contract has a value of zero to both sides at inception.

As time passes, the market spread for the same reference entity and the same remaining maturity changes. If credit quality worsens, the spread widens. The buyer is paying a coupon that is now too low for the risk, so the buyer's position gains. The seller is receiving too little and has a loss. If credit quality improves, the spread tightens and the signs reverse.

To value the change since inception, think of the CDS as an annuity of spread differences. The difference between the current market spread and the market spread at inception is paid over the remaining life. The present value of that annuity is roughly the spread change times the risk duration (also called the risky annuity or CDS duration) times the notional. This is the same logic as bond price change ≈ −duration × yield change. The upfront payment made at inception is already settled, so it is not part of this gain or loss.

Keep two bases separate. The change in value since inception uses the change in the market spread: Δspread = current market spread − market spread at inception. The total mark-to-market relative to the coupon uses the fixed coupon (100 or 500 bps for standard contracts): (current spread − coupon) × duration. This is also how the upfront premium is quoted, as a percent of notional: price of CDS (protection seller's view) ≈ 100 − upfront premium, and upfront premium ≈ (spread − coupon) × duration.

Two more points matter. With an unchanged spread, the value moves toward zero as time passes. Risk duration shrinks, so the same spread gap is worth less. At a credit event, the protection buyer's CDS value jumps to the settlement amount, (1 − recovery rate) × notional. That is the amount the buyer receives.

Key formulas to remember

Change in CDS value since inception (approximation): ΔCDS value ≈ Δspread × risk duration × notional; Use the buyer's view. A positive result means a gain for the protection buyer and a loss for the seller. Δspread is the change in market spread since inception.
Spread change since inception: Δspread = current market spread − market spread at inception; Use the spread for the remaining maturity of the contract, not the original tenor. Do not use the coupon here.
Total MTM relative to the coupon: Total MTM ≈ (current spread − coupon) × risk duration × notional; Uses the fixed coupon (100 or 500 bps), not the original market spread. Positive means value to the protection buyer.
Upfront premium (percent of notional): Upfront premium ≈ (CDS spread − CDS coupon) × risk duration; Positive means the buyer pays the seller. Negative means the seller pays the buyer.
CDS price (per 100 notional): CDS price ≈ 100 − upfront premium (%); Quoted from the protection seller's point of view. A higher spread means a lower price.
Payout at a credit event: Payout = (1 − recovery rate) × notional; This is the loss given default, paid to the protection buyer.

How to solve CDS Valuation and Changes After Inception questions

Follow this order for any item-set question on valuing a CDS after it has been initiated.

1Identify the position: protection buyer (long CDS) or protection seller (short CDS).
2Decide the basis the question uses: gain since inception (compare with the market spread at inception) or value relative to the coupon (compare with the 100 or 500 bps coupon).
3Find the relevant starting spread and the current market spread in the vignette or exhibit.
4Compute Δspread = current − starting spread, paying attention to bps versus percent.
5Find the risk duration for the remaining life. If the vignette gives a duration for the original tenor, check whether time has passed.
6Compute value change = Δspread × duration × notional.
7Assign the sign: widening gains for the buyer and loses for the seller. Tightening does the opposite.
8If asked about the price, use price ≈ 100 − upfront premium, and check that the direction makes sense.
9If asked about time passing with no spread change, say value converges toward zero and the upfront or MTM amount shrinks.

Quickest way: Sign first, then three-number multiply

When to use it: Use for any gain/loss or mark-to-market question when spread and duration are given.

Decide the sign from the spread move and the position before you calculate anything.
Convert bps to decimals: 40 bps = 0.0040.
Multiply Δspread × duration × notional.
Eliminate options with the wrong sign, then check the size.
If the question asks for price, subtract the upfront percent from 100.

Common mistakes in CDS Valuation and Changes After Inception

Giving the gain to the protection seller when the spread widens.
Students think of the seller as the one who benefits from higher spreads, since higher spreads mean higher income.
Fix: The seller's income is fixed at the old coupon. A wider market spread means the seller is underpaid for the risk, so the seller loses.
Using the original tenor's duration after time has passed.
The vignette gives one duration figure early on and students reuse it.
Fix: Use the duration for the remaining life. It falls as maturity approaches.
Mixing up bps and percent.
Spreads are quoted in bps but formulas need decimals.
Fix: Divide bps by 10,000 before multiplying. 125 bps = 0.0125.
Mixing the two bases for the spread change.
Students compare the new spread to the standard coupon when the question asks for gain since inception, or compare it to the original market spread when the question asks for value relative to the coupon.
Fix: Read the question. For a gain since inception, use the market spread at inception; the upfront already settled the gap to the coupon. For total value relative to the coupon, use (current spread − coupon) × duration.
Saying a CDS price rises when the spread widens.
Confusing price with spread.
Fix: CDS price is quoted for the seller, so a wider spread lowers the price. Upfront premium rises when the spread widens.
Thinking value stays constant if the spread is unchanged.
Students ignore the time effect.
Fix: With a constant spread, the remaining spread gap is paid over fewer periods, so the value converges to zero by maturity.

Worked examples

Example 1

A 5-year CDS has a standard coupon of 100 bps. At inception the market spread is 140 bps and the risk duration is 4.4. The protection seller receives the upfront premium from the buyer at inception. Six months later, the market spread for the same entity is still 140 bps. (1) Compute the upfront premium at inception. (2) Compute the CDS price per 100 notional at inception. (3) With the spread unchanged, explain what happens over time to the coupon-relative value (the upfront-equivalent amount) and to the price.

Show the solution

(1) Upfront premium ≈ (0.0140 − 0.0100) × 4.4 = 0.0040 × 4.4 = 0.0176 = 1.76% of notional.
The spread is above the coupon, so the buyer pays the seller 1.76% at inception. After this payment, the contract has zero value to both sides.
(2) CDS price ≈ 100 − 1.76 = 98.24.
(3) The coupon-relative value is (current spread − coupon) × risk duration. It is the upfront-equivalent amount, and the buyer has already paid it. With the spread unchanged at 140 bps, the 40 bps gap stays the same, but the remaining life is shorter, so risk duration is lower. The same gap is paid over fewer periods, so the coupon-relative value shrinks from 1.76% of notional toward zero, and the price rises from 98.24 toward 100 as maturity approaches. The buyer's net position after paying the upfront is worth zero at inception, and with no spread change it converges to par rather than producing a gain.

Answer: (1) Upfront premium is about 1.76% of notional, paid by the buyer to the seller at inception. (2) Price is about 98.24. (3) With the spread unchanged at 140 bps, the coupon-relative (upfront-equivalent) value shrinks from 1.76% toward zero and the price moves toward 100 as maturity nears.

Example 2

An analyst holds a position as protection buyer on a 5-year CDS with a notional of ₹50,00,00,000 (treat the amounts in a single currency). The market spread at inception was 200 bps, and any upfront payment was settled then. One year later, the market spread for the 4-year CDS on the same entity is 260 bps. The risk duration of the 4-year CDS is 3.6. (1) Estimate the percent change in the CDS value since inception. (2) Estimate the gain or loss for the buyer since inception. (3) State who benefits if the spread had narrowed to 170 bps.

Show the solution

The question asks for the change since inception, so compare the current market spread with the market spread at inception. The upfront is already paid and is not part of this change.
Δspread = 260 − 200 = 60 bps = 0.0060.
(1) Percent change ≈ 0.0060 × 3.6 = 0.0216 = 2.16% of notional.
(2) Gain = 0.0216 × ₹50,00,00,000 = ₹1,08,00,000. The buyer gains because the spread widened.
(3) If the spread narrowed to 170 bps, Δspread = −30 bps, so the buyer would lose 0.0030 × 3.6 = 1.08% of notional, and the seller would gain.

Answer: (1) About 2.16% of notional. (2) The buyer gains about ₹1,08,00,000 since inception. (3) The protection seller would benefit from narrowing.

Exam tips

Write the sign of the gain or loss before computing. This avoids the most common wrong answers.
Check whether the vignette gives duration for the original tenor or for the remaining life. Use the remaining life.
Remember that CDS price moves opposite to spread. Upfront premium moves with spread.
Check which basis the question uses: change since inception (market spread at inception) or value relative to the coupon (100 or 500 bps).
Expect a conceptual question on convergence: with no spread change, value tends to zero, and at a credit event the protection buyer's value jumps to the settlement amount, (1 − recovery rate) × notional.
Convert bps to decimals before multiplying. Many wrong options are off by a factor of 100.

CDS Valuation and Changes After Inception: frequently asked questions

How do I calculate the change in CDS value after inception?

Multiply the spread change by the risk duration and the notional. Δspread is the current market spread minus the market spread at inception. A positive result is a gain for the protection buyer and a loss for the seller.

Who gains when the CDS spread widens?

The protection buyer gains. The buyer pays a fixed coupon that is now below the market rate for that credit risk. The protection seller has a mark-to-market loss.

What does convergence to par mean for a CDS?

If the spread does not change, the value of the CDS moves toward zero as maturity approaches, so the price moves toward 100. Risk duration falls over time, so the same spread gap is worth less.

Why is CDS price equal to 100 minus the upfront premium?

The price is quoted from the protection seller's point of view, like a bond price. When the spread is above the coupon, the buyer pays an upfront premium to the seller, so the price is below 100.