How credit products work

You'll come away knowing what a credit product pays, how the market quotes it, and what its price depends on, so the reference pages read as a list of arguments rather than a puzzle. Nothing here is a step you need to follow; the how-to guides do that.

What every credit product shares

Every credit product turns on one question: does a name survive to a date? A survival curve gives that probability for every date. Its slope is the hazard rate, the chance of default in the next instant given survival so far. Most desks mark a flat or piecewise-flat hazard from the name's quoted spreads, as credit calibration shows.

When a name defaults, holders of its debt recover part of what they're owed. The recovery is that fraction, and one minus it is the loss on default. A survival curve is always pinned with the recovery its quotes assumed: the same spread read with a different recovery implies a different hazard.

A credit contract has two legs. The premium leg pays a running coupon while the name survives. The protection leg pays the loss if it defaults. The contract is quoted by its par spread, the coupon at which the two legs are worth the same. On a flat hazard the par spread sits close to the hazard times the loss on default, the rule of thumb desks call the credit triangle.

A survival curve belongs to one issuer, one seniority, one documentation clause and one currency, written ACME/SeniorUnSec/XR14/USD. Senior and subordinated debt of the same issuer recover differently, and two restructuring clauses pay on different events, so each gets its own curve.

Single-name CDS

A credit default swap transfers one issuer's default risk. Most contracts trade on standard terms: a running coupon of 100bp or 500bp, quarterly payments on the 20th of March, June, September and December, and maturities rolled to the 20th of June or December. Because the coupon is fixed, a trade at any other spread settles the difference upfront, and the par spread is what desks still quote.

When a name defaults between coupon dates, the buyer owes the premium accrued since the last one. The standard pays it in proportion to the time accrued. Two alternatives appear in contracts: halfway, as if every default fell mid-period, which lands close to the standard; and none, which pays nothing and so leaves the buyer the most protection for the premium.

Index CDS

An index CDS buys or sells protection on a standard basket of names, such as the 125 investment-grade names of CDX.NA.IG, in one contract. It is the most liquid credit instrument.

Every six months, on the 20th of March and September, a family rolls a new series with its membership refreshed. The newest series is on the run and trades most. A five-year contract matures three months after its series' roll plus five years, and keeps that maturity once it goes off the run.

An index trades on its own spread, so desks mark a survival curve for the index itself, under the series' identity CDX.NA.IG.47v1. That curve and the curves of its 125 names need not agree: the index usually trades a little through or wide of the portfolio of its names, and desks measure the gap, the index basis, by comparing the two.

CDS options

A CDS option, or credit swaption, is the right to enter a CDS at a strike spread on a future date. A payer is the right to buy protection, which gains when spreads widen; a receiver is the right to sell it.

A single-name option knocks out: if the name defaults before expiry, the option disappears, because protection on a defaulted name can't be bought. Options are priced with Black's model on the forward par spread, scaled by the risky annuity, and quoted by the vol of that forward spread. A payer less a receiver at the same strike is a forward CDS at that strike, whatever the vol, which makes put–call parity a check on the bookkeeping rather than on the inputs.

Credit events

A credit event, such as a default, a bankruptcy or a qualifying restructuring, triggers settlement on every contract referencing the name. An auction fixes the final price, the recovery every contract settles on.

An index position then receives protection on the defaulted name's weight and pays the premium accrued on that weight since the last coupon. The index carries on without the name under a new version: v1 becomes v2, its factor reduced by the name's weight.

A tranche on the same pool is eroded from the bottom by the loss, and its attachment points are restated on the surviving pool. The amount recovered is written off the top of the structure, so only the most senior tranche records a write-down.

Tranches and correlation

A synthetic CDO tranche takes the losses of an index pool between an attachment and a detachment point. The equity tranche absorbs the first losses and pays the widest spread; senior tranches are hit only after many defaults. What prices a tranche, beyond the index curve, is how much defaults cluster.

The standard model ties each name's default to one common market factor and one factor of its own: the one-factor copula. Given the common factor, names default independently, so the pool's loss distribution is easy to compute; the correlation sets how much weight the common factor carries. With a Gaussian copula, joint defaults are rare. A double-t copula, with fatter tails, moves value between the equity tranche and the senior end. A recovery that falls in bad states of the market does the same from the other side.

The market quotes tranches by base correlation: for each detachment point, the one correlation at which a tranche from zero to that point prices to market. A tranche between two points is then the difference of two such base tranches, each at its own correlation. The default reading treats the pool as very large; a finite pool of identical names, where the number of defaults is binomial, converges to it as the names increase.

Nth-to-default

An nth-to-default swap buys protection on a small basket that pays only when the n-th name defaults. A first-to-default pays on whichever name goes first. Baskets are bespoke, typically three to ten names on standard CDS terms.

Two bounds hold without computing anything. The first default is at least as likely as any one name's, and no more likely than all of them added up. So a first-to-default spread lies between the widest single-name spread and the sum of them. A second default needs a first, so a second-to-default is cheaper than a first-to-default. Where between those bounds the price lands depends on the correlation, which can be a contract term or a market input pinned under its own key.

Credit-linked notes and swaps

A credit-linked note is a bond whose payments depend on a reference name surviving. The investor pays the face up front, receives a coupon while the name survives, gets the face back at maturity if it still does, and receives the recovery if it doesn't. It is a funded way to sell protection, for investors who can't trade CDS. Its value splits exactly into the coupons, the redemption and the recovery, each weighted by survival.

A credit-linked swap generalises the idea to any set of legs. Each leg carries a role: an independent leg pays whatever happens, a contingent leg only while the name survives, and a default or recovery leg pays on default, scaled by the loss or the recovery. Where default can't happen, a contingent leg is worth exactly its independent value.