The Mathematics of Financial Modelingand Investment Management

22-Credit Risk Model Derivs Page 681 Wednesday, February 4, 2004 1:12 PM

Credit Risk Modeling and Credit Default Swaps 681

This may apply when a credit default swap has been entered into on a ref-

erence entity rather than a specific obligation issued by that entity (i.e.,

when there is a reference entity rather than a reference obligation).

Where more than one deliverable obligation is specified, the protection

buyer will invariably deliver the one that is the cheapest on the list of eligi-

ble deliverable obligations. This gives rise to the concept of the cheapest-

to-deliver. In practice, the protection buyer will deliver the cheapest-to-

deliver bond from the deliverable basket. This delivery option has debat-

able value in theory, but significant value in practice.

The standard contract for a single-name credit default swap in the

interdealer market calls for a quarterly payment of the swap premium.

Typically, the swap premium is paid in arrears. The quarterly payment is

determined using one of the day count conventions in the bond market.

A day count convention indicates the number of days in the month and

the number of days in a year that will be used to determine how to pro-

rate the swap premium to a quarter. The day count convention used for

credit default swaps is actual/360. A day convention of actual/360

means that to determine the payment in a quarter, the actual number of

days in the quarter are used and 360 days are assumed for the year.

Basket Default Swaps

In a basket default swap, there is more than one reference entity. Typically,

in a basket default swap, there are three to five reference entities. There are

different types of basket default swap. They are classified as follows:

■ Nth to default swaps

■ Subordinate basket default swaps

■ Senior basket default swaps

Below we describe each type.

Nth to Default Swaps

In an Nth-to-default swap, the protection seller makes a payment to the

protection buyer only after there has been a default for the Nth refer-

ence entity and no payment for default of the first (N – 1) reference enti-

ties. Once there is a payout for the Nth reference entity, the credit

default swap terminates. That is, if the other reference entities that have

not defaulted subsequently do default, the protection seller does not

make any payout.

For example, suppose that there are five reference entities. In a first-

to-default basket swap a payout is triggered after there is a default for

only one of the reference entities. There are no other payouts made by the