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 .
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 .