Correlation stress testing for value-at-risk

ABSTRACT The correlation matrix is of vital importance for value-at-risk (VAR) models in the financial industry. Risk managers are often interested in stressing a subset of market factors within large-scale risk systems containing hundreds of market variables. Correlations change during crisis times and the correlation matrix should be modified accordingly for such scenarios. This paper presents two new methods for stressing (perturbing) terms locally in a symmetric positive definite correlation matrix. The first method gives the exact bounds in closed form for stressing a single term in the matrix on the condition that it remains positive definite. An iterative sequential application of this method extends it to stress locally a group of correlations. The second method proposes a computationally efficient near-optimal solution to the problem of finding the closest positive semidefinite correlation matrix to a non-positive definite target matrix which results from local stressing of the original matrix.