FRM Exam Part II · Credit Risk

Credit Derivatives and Securitization for FRM Part II

Updated 11 October 2026 · Fact-checked

Credit derivatives, mainly credit default swaps, transfer default risk in return for a fee. Securitization pools loans and slices the losses into tranches: equity absorbs losses first, senior last. To solve questions, find the pool loss, apply attachment and detachment points, and price a CDS with spread ≈ hazard rate × (1 − recovery).

Understand Credit Derivatives and Securitization

A credit default swap (CDS) is insurance-like protection on a reference entity. The protection buyer pays a regular spread (premium). If a credit event happens, such as bankruptcy or failure to pay, the seller pays the buyer the loss: notional × (1 − recovery rate). Settlement is physical (buyer delivers the defaulted bond for par) or cash (seller pays par minus the market value after default).

A CDS spread reflects the market's view of default risk. The credit triangle links the three pieces: spread ≈ default hazard rate × (1 − recovery rate). A full valuation sets the present value of the premium leg equal to the present value of the protection leg. The premium leg is the spread times a risky annuity, which is the discounted sum of payments weighted by survival probability. The protection leg is (1 − R) times discounted default probabilities.

A total return swap (TRS) is different. The total return receiver gets all the cash flows and price changes on a reference asset and pays a floating rate plus a spread. So a TRS transfers market risk and credit risk together, even when no default happens. A CDS pays only on a credit event.

Securitization pools loans or bonds into a special purpose vehicle (SPV) that is legally separate from the originator. The SPV issues notes in tranches. Losses hit the lowest tranche first (equity), then mezzanine, then senior. A tranche is defined by its attachment point (where losses start to hit it) and detachment point (where it is wiped out). Subordination, overcollateralization, excess spread and reserve accounts are forms of credit enhancement.

Tranching does not remove risk from the pool. It reallocates it. The expected loss of the pool equals the sum of the expected losses of the tranches. Default correlation drives how the risk is shared. Higher correlation lowers the risk of the equity tranche and raises the risk of the senior tranche, because defaults cluster. A synthetic CDO takes its credit exposure through CDS instead of owning the loans. The 2007-2009 crisis showed how mispriced correlation and layered structures (such as CDO-squared) can turn small pool losses into large senior losses.

Key formulas to remember

CDS payout on credit event: Payout = Notional × (1 − Recovery rate); Also equals notional × (1 − market price as a fraction of par) for cash settlement.
Credit triangle: Spread ≈ λ × (1 − R), so λ ≈ Spread ÷ (1 − R); λ is the annual hazard rate. It is an approximation that assumes a flat hazard rate and spread. Spread is in decimals (120 bp = 0.012).
CDS valuation (par spread): s × Risky annuity = (1 − R) × PV of default-weighted discount factors; Premium leg PV equals protection leg PV at the par spread.
Value of an existing CDS (approximate): Value to buyer ≈ (Current spread − Contract spread) × Notional × Risky annuity; Positive for the protection buyer if spreads have widened.
Cumulative default probability (constant hazard): P(default by T) = 1 − e^(−λT); Survival probability is e^(−λT).
Tranche loss: Tranche loss (as % of tranche) = min[max(L − A, 0), D − A] ÷ (D − A); L = pool loss %, A = attachment point, D = detachment point.
Tranche size: Tranche size = (D − A) × Pool notional; Dollar tranche loss = tranche loss % × tranche size.
Conservation of expected loss: Pool expected loss = Σ (tranche expected loss in pool terms); Correlation changes the split between tranches, not the total.
Correlation effect on tranches: Higher correlation → equity tranche risk falls; senior tranche risk rises; Mezzanine behaviour is mixed and depends on the structure.

How to solve Credit Derivatives and Securitization questions

Use this order for any credit derivative or securitization question. It keeps you from mixing up risk transfer, pricing and loss allocation.

1Identify the instrument: single-name CDS, index CDS, TRS, cash CDO, synthetic CDO or a plain ABS/MBS structure.
2Identify who bears which risk. A CDS buyer is short credit. A CDS seller is long credit. A TRS receiver is long the asset, including market risk.
3Write down the inputs in consistent units: notional, spread in decimals, recovery rate, tenor, attachment and detachment points.
4For pricing, use the credit triangle for a quick answer: λ = spread ÷ (1 − R). Then use 1 − e^(−λT) for default probability. Use the full leg-matching only if the question gives discount factors and survival probabilities.
5For tranches, compute the pool loss in dollars or percent, subtract the attachment point, cap at the tranche width, then divide by the width.
6Check the answer: tranche losses must sum to pool loss, and a junior tranche must never lose less in percent terms than a more senior one for the same pool loss.
7State the interpretation: what the number says about who loses, and how correlation, recovery or spread changes would move it.

Quickest way: Credit triangle and waterfall shortcut

When to use it: Use it when the question gives a spread, a recovery rate and a pool loss, and asks for a hazard rate, default probability or tranche loss.

Spread ÷ (1 − R) gives the hazard rate. Convert basis points first.
Multiply by tenor and use 1 − e^(−λT). For small numbers, λT is close enough to eliminate options.
For a tranche, subtract A from pool loss, cap at D − A, divide by D − A.
For direction questions, remember: more correlation helps equity, hurts senior; wider spread helps the protection buyer; a TRS carries market risk, a CDS does not.

Common mistakes in Credit Derivatives and Securitization

Using the spread as the default probability.
Both look like small annual percentages.
Fix: Divide the spread by (1 − R) to get the hazard rate. A 120 bp spread with 40% recovery implies 2%, not 1.2%.
Dividing tranche loss by the pool size instead of the tranche size.
The pool loss is given as a percentage of the pool, so students stop there.
Fix: Compute the loss in pool terms first, then divide by the tranche width D − A to get the loss as a percentage of the tranche.
Saying higher correlation makes every tranche riskier.
Correlation is linked with crises in memory.
Fix: Higher correlation reduces equity tranche risk and raises senior tranche risk. Expected pool loss does not change.
Treating a TRS like a CDS.
Both are called credit derivatives and both reference an asset.
Fix: A CDS pays only on a credit event. A TRS passes on all price moves and income, so the receiver bears market risk even without default.
Forgetting recovery in the CDS payout.
Students think the seller pays the full notional.
Fix: The seller pays notional × (1 − R), or par minus the post-default price. In physical settlement the buyer delivers the bond and receives par.
Thinking tranching removes credit risk from the system.
Senior tranches get high ratings, so risk seems gone.
Fix: Tranching only redistributes pool losses. Senior tranches still lose if pool losses exceed the attachment point, as happened in the subprime crisis.

Worked examples

Example 1

A 5-year CDS on a corporate issuer trades at a spread of 120 bp. Assume a recovery rate of 40% and a constant hazard rate. Estimate the hazard rate and the probability of default within 5 years. If a credit event occurs on a $20 million notional and the defaulted bond trades at 35% of par, what does the protection seller pay?

Show the solution

Convert the spread: 120 bp = 0.012.
Hazard rate: λ ≈ 0.012 ÷ (1 − 0.40) = 0.012 ÷ 0.60 = 0.02, or 2% a year.
Cumulative default probability: 1 − e^(−0.02 × 5) = 1 − e^(−0.10).
e^(−0.10) ≈ 0.9048, so the probability is 1 − 0.9048 ≈ 0.0952, about 9.5%.
Cash settlement payout: $20 million × (1 − 0.35) = $20 million × 0.65 = $13 million.

Answer: Hazard rate about 2% a year; 5-year default probability about 9.5%; the protection seller pays $13 million. Note the payout uses the actual post-default price (35%), not the 40% recovery used for pricing.

Example 2

A CDO is backed by a $1 billion loan pool. The mezzanine tranche attaches at 5% and detaches at 15%. Pool losses reach 8%. Then losses reach 20%. Find the mezzanine tranche loss in dollars and as a percentage of the tranche in each case.

Show the solution

Tranche width: 15% − 5% = 10% of $1 billion = $100 million.
Case 1, pool loss 8%: loss above attachment = 8% − 5% = 3%. This is below the 10% width, so no cap applies.
Dollar loss: 3% × $1 billion = $30 million.
As a share of the tranche: 3% ÷ 10% = 30%, or $30 million ÷ $100 million = 30%.
Case 2, pool loss 20%: loss above attachment = 15%, which exceeds the width of 10%, so the tranche loss is capped at 10%.
Dollar loss: $100 million, which is 100% of the tranche. The remaining 5% of pool loss ($50 million) falls on the senior tranche above 15%.

Answer: At 8% pool loss, the mezzanine tranche loses $30 million (30% of the tranche). At 20% pool loss, it is wiped out: $100 million (100%), and the senior tranche absorbs a further $50 million.

Exam tips

Convert basis points to decimals before any calculation. Many wrong options are built from a unit slip.
When a question gives pool loss and attachment points, draw a quick bar from 0% to 100% and mark A and D. It prevents capping errors.
Read whether the question asks for loss as a percentage of the pool or of the tranche. Options often include both.
Know the CDS versus TRS contrast cold: credit event only versus total economic return. Questions on this are common and quick marks.
For correlation questions, think of equity as long correlation and senior as short correlation, and remember that expected pool loss stays the same.

Practice questions from Credit Risk

Credit Derivatives and Securitization in other exams

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

Credit Derivatives and Securitization: frequently asked questions

How do I price a credit default swap for FRM Part II?

For quick questions, use the credit triangle: spread ≈ hazard rate × (1 − recovery). For fuller valuation, set the present value of premium payments (spread × risky annuity) equal to the present value of expected protection payments. The spread that makes them equal is the par spread.

How does CDO tranching work?

The pool's losses are allocated from the bottom up. The equity tranche takes the first losses, then mezzanine, then senior. Each tranche has an attachment and a detachment point, and it loses only when pool losses pass its attachment point.

What is the difference between a CDS and a total return swap?

A CDS pays only if a credit event happens on the reference entity. A total return swap passes on all income and price changes of the reference asset in exchange for a floating payment, so it transfers market risk as well as credit risk.

What does default correlation do to CDO tranches?

Higher correlation makes defaults cluster. That lowers the risk of the equity tranche, because zero-loss outcomes become more likely, and raises the risk of senior tranches, because extreme pool losses become more likely. The total expected loss of the pool does not change.

What is a synthetic CDO?

A synthetic CDO gets its credit exposure by selling protection through CDS rather than holding loans or bonds. Investors in the tranches take on the losses from credit events on the reference names, using the same attachment and detachment logic.