Credit Derivatives: CDS, CDOs, and the Products That Blew Up

If you hold a bond and the issuer might default, you want insurance. That is the basic idea behind credit derivatives. You pay someone a regular premium, and if the bad thing happens, they pay you. Chapter 41 of Wilmott’s book walks through the main types of credit derivatives, from simple default swaps to the multi-name products that helped blow up the global financial system in 2008.

Wilmott himself drops a prophetic warning in this chapter. When discussing multi-name credit derivatives and copulas, he writes: “some of these instruments and models being used for these instruments fill me with some nervousness and concern for the future of the global financial markets.” This was published before the crisis. The man saw it coming.

What Are Credit Derivatives?

Credit derivatives are contracts between two parties whose cashflows depend on the credit behavior of some third party. The third party does not even need to know the derivatives exist.

Three defining features:

1. Payoffs triggered by default of a reference entity
2. Payoffs linked to mark-to-market returns on a specific security
3. Payoffs linked to credit rating changes assessed by rating agencies

Credit derivatives unbundle credit risk from everything else. Before these products existed, if you bought a corporate bond you got interest rate risk, credit risk, and liquidity risk all wrapped together. Credit derivatives let you isolate and trade just the credit piece.

Who Uses Them?

Banks use them to hedge specific default exposures, diversify loan portfolio risk, free up credit lines, and manage capital requirements.

Investors and hedge funds use them to access new asset classes, create synthetic high-yield positions, exploit mispricing, and get leverage.

Corporates use them to hedge supplier and customer credit risk, and to manage project risk including sovereign exposure.

The Credit Default Swap (CDS)

The CDS is the bread and butter of the credit derivatives market. It works like insurance.

The protection buyer pays regular premiums (quoted in basis points per notional) to the protection seller. These premiums continue until either the contract matures or a credit event occurs.

The protection seller makes a contingent payment if a credit event occurs. Settlement can be physical (deliver the defaulted bond, receive par) or cash (receive the difference between par and recovery value).

A credit event includes: failure to make payments, bankruptcy, debt restructuring, or distressed rescheduling. There is usually a “materiality” clause confirming the default is real.

The CDS changed everything. You could bet on default without owning any bonds. You could hedge credit exposure without selling anything. The reference entity did not even need to know.

Key pricing factors: probability of default, maturity, expected recovery value, and correlation between reference entity and swap counterparty. That last one is critical. Do not buy protection on a Japanese bank from another Japanese bank.

Total Return Swaps

Total return swaps (TRS) transfer ALL risks of owning an asset, not just credit risk. The payer passes all cashflows and appreciation to the receiver, who pays LIBOR plus a spread and covers any depreciation.

The main appeal is leverage. The receiver gets economic exposure without buying the asset. Even after posting collateral, the enhanced return on regulatory capital can be enormous.

Basket Products and Spread Derivatives

First to default products are like CDS but on a basket of 10 or so names. The first entity to default triggers the payoff. Nth to default triggers on the Nth default and is cheaper because more defaults must occur. Pricing depends heavily on correlation between names.

Some credit derivatives do not require default at all. Credit spread options pay off based on changes in the yield spread between risky and risk-free bonds. Exchange options give you the right to swap a risky bond for a quantity of risk-free bonds.

Payment on Change of Rating

These are contracts that trigger on credit rating changes, not default. Wilmott uses the Korea Development Bank note as a real-world example.

In June 1997, KDB issued a floating rate note paying LIBOR plus 18.75 basis points. The note included a put feature: the holder could sell it back to KDB at par if the bank’s rating fell below A- (S&P) or A3 (Moody’s).

What happened? In December 1997, Moody’s cut KDB from A3 to Baa2. S&P dropped it from A- to BBB-. This triggered the put. Most bondholders exercised, costing KDB $300 million at a time when South Korea was in a severe liquidity crisis. Korea was later demoted to junk bond status.

The pricing of such contracts uses the Markov chain model from Chapter 40. The triggering condition (reaching a specific rating) acts like a barrier in an option. Think of it as a knock-in option where the “barrier” is a credit rating level rather than a stock price.

Pricing with Stochastic Hazard Rate

For complex credit derivatives, constant hazard rate is not enough. With constant $p$, the risky bond is a deterministic multiple of the risk-free bond, making exchange options trivially priced. The fix: make $p$ stochastic. Then the exchange option becomes a real derivatives pricing problem, mathematically identical to a put on a zero-coupon bond but with $p$ replacing $r$.

Copulas: The Multi-Name Problem

When you have many underlying names (think 100+ companies in a CDO), you need a way to model their joint default behavior. This is where copulas enter.

A copula function separates two things: the probability of default for each individual name (the marginal distributions) and the dependence structure between names. You can calibrate each name independently and then combine them through the copula.

Mathematically, take $N$ random variables with cumulative distributions $F_1(x_1), \ldots, F_N(x_N)$. The copula $C$ defines the joint distribution:

$$F(x_1, \ldots, x_N) = C(F_1(x_1), \ldots, F_N(x_N))$$

Sklar’s theorem says any multivariate distribution can be written this way. Different copula functions give different dependence structures:

• Bivariate normal copula: Uses the standard normal joint distribution. This is the Gaussian copula that became famous (and infamous).
• Gumbel-Hougaard copula: Good for extreme value distributions, higher tail dependence than Gaussian.
• Frank, Clayton, Archimedean copulas: Each with its own dependence characteristics.

The tail index tells you how likely extreme joint events are. It is the probability that both variables take extreme values simultaneously. Different copulas give very different tail behavior, and this matters enormously in practice.

Collateralized Debt Obligations (CDOs)

CDOs are where the multi-name credit world goes big. A CDO gives protection against losses in a portfolio of typically hundreds of companies.

The portfolio’s aggregate losses are split into tranches. Each tranche has an attachment point (where you start losing money) and a detachment point (where your tranche is fully wiped out). A typical structure:

The 0-3% tranche (equity tranche) gets hit first. Its upfront premium of 42% reflects the high probability of loss. The 15-30% tranche (senior tranche) needs catastrophic portfolio-wide losses to be affected, so it is cheap.

The Correlation Problem

CDO pricing requires modeling both individual default probabilities AND the correlation between names. Standard practice uses a Gaussian copula with a single correlation parameter. This is probably at least one simplification too far, as Wilmott notes.

The implied correlation backed out from market prices differs by tranche, creating a “correlation smile” analogous to the volatility smile in options. Worse, sometimes there are TWO implied correlations for a given tranche, or NONE at all.

Why This Should Scare You

Wilmott draws a parallel to barrier options. In a knock-out call, sometimes volatility helps (getting into the money) and sometimes it hurts (knocking you out). Same competing effects with CDO correlation. If only the “bad” correlation shows up, prices crash far below what the Gaussian copula predicts. With hundreds of underlying names, exploring these scenarios becomes nearly impossible.

Wilmott’s Warning

Wilmott says default-risk modeling is “far from satisfactory.” He makes an important distinction: if you trade a risky bond short-term, the market’s subjective view of default risk determines your profit. If you hold to maturity, only the actual objective risk matters. These are different things, and the gap between your model and the market’s is where both opportunities and disasters live.

The credit derivatives market grew from nearly nothing to trillions in a decade. The risk tools grew much more slowly. Wilmott saw the gap. The 2008 crisis proved him right.

This is part of a series covering “Paul Wilmott on Quantitative Finance”. Next up: RiskMetrics and CreditMetrics.

Previous: Credit Risk: Modeling the Chance of Default.