The Mathematics of Financial Modelingand Investment Management

22-Credit Risk Model Derivs Page 682 Wednesday, February 4, 2004 1:12 PM

682 The Mathematics of Financial Modeling and Investment Management

protection seller even if the other four reference entities subsequently have

a credit event. If a payout is triggered only after there is a second default

from among the reference entities, the swap is referred to as a second-to-

default basket swap. So, if there is only one reference entity for which

there is a default over the tenor of the swap, the protection seller does not

make any payment. If there is a default for a second reference entity while

the swap is in effect, there is a payout by the protection seller and the

swap terminates. The protection seller does not make any payment for a

default that may occur for the three remaining reference entities.

Subordinate and Senior Basket Credit Default Swaps

In a subordinate basket default swap there is (1) a maximum payout for

each defaulted reference entity and (2) a maximum aggregate payout

over the tenor of the swap for the basket of reference entities. For exam-

ple, assume there are five reference entities and that (1) the maximum

payout is $10 million for a reference entity and (2) the maximum aggre-

gate payout is $10 million. Also assume that defaults result in the fol-

lowing losses over the tenor of the swap:

Loss result from default of first reference entity = $6 million

Loss result from default of second reference entity = $10 million

Loss result from default of third reference entity = $16 million

Loss result from default of fourth reference entity = $12 million

Loss result from default of fifth reference entity = $15 million

When there is a default for the first reference entity, there is a $6

million payout. The remaining amount that can be paid out on any sub-

sequent defaults for the other four reference entities is $4 million. When

there is a default for the second reference entity of $10 million, only $4

million will be paid out. At that point, the swap terminates.

In a senior basket default swap there is a maximum payout for each

reference entity but the payout is not triggered until after a specified

threshold is reached. To illustrate, again assume there are five reference

entities and the maximum payout for an individual reference entity is

$10 million. Also assume that there is no payout until the first $40 mil-

lion of default losses (the threshold). Using the hypothetical losses

above, the payout by the protection seller would be as follows. The

losses for the first three defaults is $32 million. However, because the

maximum loss for a reference entity, only $10 million of the $16 million

is applied to the $40 million threshold. Consequently, after the third

default, $26 million ($6 million + $10 million + $10 million) is applied