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The credit default swap (CDS) is the most widely used credit derivative. It is an agreement between a protection buyer and a protection seller whereby the buyer pays a periodic fee in return for a contingent payment by the seller upon a credit event (such as a certain default) happening in the reference entity. A CDS is often used like an insurance policy, or hedge for the holder of a corporate bond. The typical term of a CDS contract is five years, although being an over-the-counter derivative almost any maturity is possible.

Definitions in a CDS Contract

A CDS contract typically includes a reference entity, which is the company who has issued some debt in the form of a reference obligation, usually a corporate bond. The period over which default protection extends is defined by the contract effective date and termination date. The contract nominates a calculation agent whose role is to determine when a credit event has occurred and also the amount of the payment that will be made in such an event. Another clause in a CDS contract is the restructuring clause, which determines what restructuring of the reference entity's debt will trigger a credit event. For example a company that is experiencing financial trouble may decide to extend the maturity of its bonds and therefore defer its payments. Depending on the restructuring specified in a CDS this may or may not trigger a credit event. Generally a contract that is more lax in its criteria for default is more risky and therefore more expensive. Another factor that affects the quote on a CDS contract is the debt seniority of the reference obligation. In the event of a company becoming bankrupt bonds that are issued as senior debt are more likely to be paid back than bonds issued as subordinated, or junior debt, hence junior debt trades at a greater credit spread than senior debt.

Sellers of CDS contracts will give a par quote for a given reference entity, seniority, maturity and restructuring e.g. a seller of CDS contracts may quote the premium on a 5 year CDS contract on Ford Motor Company senior debt with modified restructuring as 100 basis points. The par premium is calculated so that the contract has zero present value on the effective date. This is because the expected value of protection payments is exactly equal and opposite to the expected value of the fee or coupon payments. The most important factor affecting the cost of protection provided by a CDS is the credit quality (often proxied by the credit rating) of the reference obligation. Lower credit ratings imply a greater risk that the reference entity will default on its payments and therefore the cost of protection will be higher.

The spread of a CDS should trade closely with that of the underlying cash bond. Cash bond refers to the reference entity. Misalignments in spreads may occur due to technical minutia such as specific settlement differences, shortages in a particular underlying instrument, and the existence of buyers constrained from buying exotic derivatives.

The settlement and processing of a CDS contract is currently the subject of investigation by the SEC. In 2005, the SEC ruled that major CDS dealers must upgrade their systems to reduce the backlog of "unprocessed" CDS contracts. As of January 1, 2006, banks have not been able to fully comply.

Example

A pension fund owns 10 million euros worth of a 5 year bond issued by Risky Corporation. In order to manage their risk of losing money if Risky Corporation defaults on its debt they buy a CDS from Derivative Bank on a nominal of 10 million euros which trades at 200 basis points. In return for credit protection the pension fund pays 2% of 10 million (200,000 euros) as quarterly payments of 50,000 euros to Derivative Bank. If Risky corporation does not default on its bond payments the pension fund makes quarterly payments to Derivative Bank for five years and receives its 10 million loan back after 5 years from the Risky Corporation. If Risky Corporation defaults on its debt 3 years into the CDS contract then the premium payments would stop and Derivative Bank would ensure that the pension fund is refunded for its loss of 10 million euros.

Levels and flows

The Bank for International Settlements reported the notional amount on outstanding credit forwards and swaps to be $3.846 trillion in end-June 2004, up from $536 billion at the end of June 2001.

The Office of the Comptroller of the Currency reported the notional amount on outstanding credit derivatives from 667 reporting banks to be $1.909 trillion.

See also

• Credit derivative

External links

ISDA CDS Template Contract

• 2003 ISDA Credit Derivatives Template

Reporting

• BIS - Regular Publications
• OCC - Quarterly Derivatives Fact Sheet

Theory

A credit default swap is priced using a model that takes three inputs: the issue premium, the credit curve for the reference entity and the Libor curve. If default events never occurred the price of a CDS would simply be the sum of the discounted premium payments. So CDS pricing models have to take into account the possibility of a default occurring some time between the effective date and maturity date of the CDS contract. For the purpose of explanation we can imagine the case of a one year CDS with effective date ${\displaystyle t_{0}}$ with four quarterly premium payments occurring at times ${\displaystyle t_{1}}$, ${\displaystyle t_{2}}$, ${\displaystyle t_{3}}$, and ${\displaystyle t_{4}}$. If the nominal for the CDS is ${\displaystyle N}$ and the issue premium is ${\displaystyle c}$ then the size of the quarterly premium payments is ${\displaystyle Nc/4}$. If we assume for simplicity that defaults can only occur on one of the payment dates then there are five ways the contract could end: either it does not have any default at all, so the four premium payments are made and the contract survives until the maturity date, or a default occurs on the first, second, third or fourth payment date. To price the CDS we now need to assign probabilities to the five possible outcomes, then calculate the present value of the payoff for each outcome. The present value of the CDS is then simply the present value of the five payoffs multiplied by their probability of occurring.

This is illustrated in the following tree diagram where at each payment date either the contract has a default event, in which case it ends with a payment of ${\displaystyle N(1-R)}$ shown in red, or it survives without a default being triggered, in which case a premium payment of ${\displaystyle Nc/4}$ is made, shown in blue. At either side of the diagram are the cashflow diagrams up to that point in time with premium payments in blue and default payments in red. If the contract is terminated the square is shown with solid shading.

At the ${\displaystyle i^{th}}$ payment, the probability of surviving over the interval ${\displaystyle t_{i-1}}$ to ${\displaystyle t_{i}}$ without a default payment is ${\displaystyle p_{i}}$ and the probability of a default being triggered is ${\displaystyle 1-p_{i}}$. The calculation of present value, given discount rates of ${\displaystyle \delta _{1}}$ to ${\displaystyle \delta _{4}}$ is then

Description	Premium Payment PV	Default Payment PV	Probability
No defaults	${\displaystyle {\frac {Nc}{4}}(\delta _{1}+\delta _{2}+\delta _{3}+\delta _{4})}$	${\displaystyle 0}$	${\displaystyle p_{1}\times p_{2}\times p_{3}\times p_{4}}$
Default at time ${\displaystyle t_{1}}$	${\displaystyle 0}$	${\displaystyle N(1-R)\delta _{1}}$	${\displaystyle 1-p_{1}}$
Default at time ${\displaystyle t_{2}}$	${\displaystyle {\frac {Nc}{4}}\delta _{1}}$	${\displaystyle N(1-R)\delta _{2}}$	${\displaystyle p_{1}(1-p_{2})}$
Default at time ${\displaystyle t_{3}}$	${\displaystyle {\frac {Nc}{4}}(\delta _{1}+\delta _{2})}$	${\displaystyle N(1-R)\delta _{3}}$	${\displaystyle p_{1}p_{2}(1-p_{3})}$
Default at time ${\displaystyle t_{4}}$	${\displaystyle {\frac {Nc}{4}}(\delta _{1}+\delta _{2}+\delta _{3})}$	${\displaystyle N(1-R)\delta _{4}}$	${\displaystyle p_{1}p_{2}p_{3}(1-p_{4})}$

External References

• Risk Neutral Pricing Theory

• Derivatives