I am trying to understand what is the default probability that exactly k default happens between times t1 and t2.

I created the following function , and call this after the matrix W of default times has been sorted:


void DoTest(Matrix& W)
{
Natural i,j;
Real t1=2;
Real t2=4;
Natural tmpsum=0;
Natural tmpsum2=0;
Natural defaultOccurences=1;
Natural test1=0;
Natural test2=0;
Natural test3=0;
Natural test4=0;
for (i=1;i<=DEFAULT_PATHS;i++)
{
tmpsum=0;
test1=0;
test3=0;
for (j=1;j<=DEFAULT_N;j++)
{
//system("PAUSE");
Real defTime=W(j,i);
//cout << "defTime=" << defTime << endl;
//if ( (defTime>t1) && (defTime<t2) )
if (defTime > t1)
{
if (defTime < t2)
{
tmpsum+=1;
}
}
if (defTime < t2)
test1++;
if (defTime < t1)
test3++;

}
if (tmpsum == defaultOccurences)
tmpsum2++;
if (test1 == defaultOccurences)
test2++;
if (test3 == defaultOccurences)
test4++;

}
cout << "no of times exactly 1 default happened before t2 = " << test2 << endl;
cout << "no of times exactly 1 default happened before t1 = " << test4 << endl;
cout << "no of times exactly 1 default happened t1 and t2 = " << tmpsum2 << endl;
Real prob1=Real(test2)/Real(DEFAULT_PATHS);
cout << "probability of exactly 1 default happened before t2 = " << prob1 << endl;
Real prob2=Real(test4)/Real(DEFAULT_PATHS);
cout << "probability of exactly 1 default happened before t1 = " << prob2 << endl;
Real prob3=Real(tmpsum2)/Real(DEFAULT_PATHS);
cout << "(method 1) prob of exactly 1 default happened between t1 and t2 = " << prob3 << endl;
Real prob4= prob1-prob2;
cout << "(method 2) prob of exactly 1 default happened between t1 and t2 = " << prob4 << endl;


}




I call it inside main() after this line:
sortColumns(W);
DoTest(W);


Now inside this function I find the probability of occurence of exactly 1 default between t1 and t2 by 2 methods:
1.probability=prob. of 1 default before time t2-prob. of 1 default before time t1
2.probability=(no. of occurences of 1 default between t1 and t2)/(no_of_paths)


I assumed they should give same value.Surprisingly, the results from method 1 and 2 are much different.

no of times exactly 1 default happened before t2 = 23289
no of times exactly 1 default happened before t1 = 14706
no of times exactly 1 default happened t1 and t2 = 14994
probability of exactly 1 default happened before t2 = 0.23289
probability of exactly 1 default happened before t1 = 0.14706
(method 1) prob of exactly 1 default happened between t1 and t2 = 0.14994
(method 2) prob of exactly 1 default happened between t1 and t2 = 0.08583
Press any key to continue . . .


method 1 gives 0.14994 while 2 gives 0.08583.

I am confused which method is wrong, aren't the probabilties additive?

when I complie by th eg++, there are error messages, "config.h", and "valarray.h" can not be found. which complier you use

hi vanna i need your some help .. i construct default correlation by copula approach .. please help me (Gaussian t Frank Clayton Gambel) i see your excel sheet but i need calculation not show graphically .. please i am waiting your response email address aliayaz18@live.com