Re: stressing correlations

Hi, everybody,

following up on our discussions on stressing correlations I made a
spreadsheet and a DLL.
Here is what it does:

in the input ("Main" sheet) the user has to specify:
-the size of the correlation matrix;
-the row and column for the element he wants to stress (row=1 and col=3 in
the example)
-the integer number N_iter;
-the original correlation matrix.

In the output (see sheet "Results") we see 2 columns:
-the first column contains possible correlation values (from -1 to 1,
N_iter+1 numbers) for the element (1,3),
-the second column contains the smallest eigenvalue for the "stressed"
correlation matrix
(which is the same as the original matrix except the elements (1,3) and (3,1)
which take values from -1 to 1).

Thus, the user can see which values for the chosen element (1,3) are
permitted
(those for which the smallest eigenvalue is positive (marked green in the
example).

The user might decide that he wants to assign the correlation which is "not
permitted" to this particular element
(the smallest eigenvalue is negative). Then the user might have a few options:
1. all the elements of the correlation matrix will be modified so that the
chosen element has the
desired correlation in it, but the change in the correlation matrix is the
"smallest" possible
(in the sense of matrix norm) (this is my next step to do for this
spreadsheet).
2. Just one column (and the corresponding row, of course) will change, while
the rest of the matrix
will stay unchanged (Kevin's suggestion). In this case the user have to
choose which column (and row)
he prefers to modify (in my example - column-row 1 or column-row 3).

We can discuss this approach with Risk Control and see how they like it. I
send you only the spreadsheet with an example now.

Tanya.