The Mathematics of Financial Modelingand Investment Management

22-Credit Risk Model Derivs Page 683 Wednesday, February 4, 2004 1:12 PM

Credit Risk Modeling and Credit Default Swaps 683

toward the threshold. When the fourth reference entity defaults, only

$10 million is applied to the $40 million threshold. At this point, $36

million is applied to the $40 million threshold. When the fifth reference

entity defaults in our illustration, only $10 million is relevant since the

maximum payout for a reference entity is $10 million. The first $4 mil-

lion of the $10 million is applied to cover the threshold. Thus, there is a

$6 million payout by the protection seller.

LEGAL DOCUMENTATION

Credit derivatives are privately negotiated agreements traded over the

counter. The International Swaps and Derivatives Association (ISDA)

has recognized the need to provide a common format for credit deriva-

tive documentation. In addition to the definitions of credit events, ISDA

developed the ISDA Master Agreement. This is the authoritative con-

tract used by industry participants because it established international

standards governing privately negotiated derivative trades (all deriva-

tives, not just credit derivatives).

The most important section of the documentation for a credit

default swap is what the parties to the contract agree constitutes a credit

event that will trigger a credit default payment. Definitions for credit

events are provided by the ISDA. First published in 1999, there have

been periodic supplements and revisions of these definitions

The 1999 ISDA Credit Derivatives Definitions (referred to as the

“1999 Definitions”) provides a list of eight possible credit events: (1)

bankruptcy; (2) credit event upon merger; (3) cross acceleration; (4)

cross default; (5) downgrade; (6) failure to pay; (7) repudiation; and (8)

restructuring. These eight events attempt to capture every type of situa-

tion that could cause the credit quality of the reference entity to deterio-

rate, or cause the value of the reference obligation to decline.

The parties to a credit default swap may include all of these events,

or select only those that they believe are most relevant. There has been

standardization of the credit events that are used in credit default swaps

in the United States and Europe. Nevertheless, this does not preclude a

credit protection buyer from including broader credit protection.

CREDIT RISK MODELING: STRUCTURAL MODELS

To value credit derivatives it is necessary to be able to model credit risk.

Models for credit risks have long existed in the insurance and corporate