The Mathematics of Financial Modelingand Investment Management

22-Credit Risk Model Derivs Page 680 Wednesday, February 4, 2004 1:12 PM

680 The Mathematics of Financial Modeling and Investment Management

the debt instrument. It could be a corporation, a sovereign government,

or a bank loan. In contrast, a reference obligation is a specific obligation

for which protection is being sought.

In a credit default swap, the protection buyer pays a fee, the swap

premium, to the protection seller in return for the right to receive a pay-

ment conditional upon the default of the reference obligation or the refer-

ence entity. Collectively, the payments made by the protection buyer are

called the premium leg; the contingent payment that might have to be

made by the protection seller is called the protection leg.

In the documentation of a trade, a default is defined in terms of a

credit event and we shall use the terms “default” and “credit event” inter-

changeably throughout this book. Should a credit event occur, the protec-

tion seller must make a payment.

Credit default swaps can be classified as follows: single-name credit

default swaps and basket swaps. We’ll discuss the difference between

these types of swaps next.

Single-Name Credit Default Swaps

The interdealer market has evolved to where single-name credit default

swaps for corporate and sovereign reference entities are standardized.

The parties to the trade specify at the outset when the credit default swap

will terminate. If no credit event has occurred by the maturity of the

credit swap, then the swap terminates at the scheduled termination date—

a date specified by the parties in the contract. However, the termination

date under the contract is the earlier of the scheduled termination date or

a date upon which a credit event occurs and notice is provided. Therefore,

notice of a credit event terminates a credit default swap.

The termination value for a credit default swap is calculated at the

time of the credit event, and the exact procedure that is followed to calcu-

late the termination value will depend on the settlement terms specified in

the contract. This will be either cash settlement or physical settlement.

A credit default swap contract may specify a predetermined payout

value on occurrence of a credit event. This may be the nominal value of

the swap contract. Alternatively, the termination value can be calculated

as the difference between the nominal value of the reference obligation

and its market value at the time of the credit event. This arrangement is

more common with cash-settled contracts.

With physical settlement, on occurrence of a credit event the buyer

delivers the reference obligation to the seller, in return for which the seller

pays the face value of the delivered asset to the buyer. The contract may

specify a number of alternative issues of the reference entity that the

buyer can deliver to the seller. These are known as deliverable obligations.