e have two instruments with
prices
and
 ,
default intensities
and
and the default times
 .
The default times are independent random variables (or conditionally
independent, see( Copula calculation for
CDO)). The default times generate filtration
 .
The
generate filtration
 .
The composition of the two filtrations
and
is
 .
Let
be the time of the first default of any asset. We aim to calculate
According to the
transformation
(see the ( Total probability rule)) it
is sufficient to compute
as if the
are deterministic functions of time. We proceed according to such recipe and
use the techniques of the section
( Distribution of Poisson
process
section),       
Suppose that we have three instruments and we are interested in calculation of
the
defined as the time of second
default.   
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