e need a
way to represent correlated default of several underlyings. Similarly to the
previous chapter (see section
( Basket credt 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. The research literature holds a variety of recipes for such
separations. The market accepted technique is the Gaussian copula. According
to Gaussian copula we will be representing the
th
underlying default time
using the
Prob
calculated as
Prob
for some properly chosen values
and correlated normal variables
.
