e need a
way to represent correlated default of several underlyings. Similarly to the
previous chapter (see section
(
Basket credit derivative
section
)) we will be separating the entire filtration
into two filtrations
and
.
The
holds jump information. The
is chosen so that the jumps described by
would be independent conditionally on
.
Such construction is what we will call "conditionally independent" credit
events. Research literature holds a variety of recipes for such separations.
The market accepted technique is Gaussian copula. According to Gaussian copula
we will be representing the
th
underlying's default time
using the
Prob
calculated as
Prob
for some properly chosen values
and correlated normal variables
.