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Correlation stress testing for value-at-risk: an unconstrained convex optimization approach

Correlation stress testing for value-at-risk: an unconstrained convex optimization approach
Correlation stress testing for value-at-risk: an unconstrained convex optimization approach
Correlation stress testing is employed in several financial models for determining the value-at-risk (VaR) of a financial institution’s portfolio. The possible lack of mathematical consistence in the target correlation matrix, which must be positive semidefinite, often causes breakdown of these models. The target matrix is obtained by fixing some of the correlations (often contained in blocks of submatrices) in the current correlation matrix while stressing the remaining to a certain level to reflect various stressing scenarios. The combination of fixing and stressing effects often leads to mathematical inconsistence of the target matrix. It is then naturally to find the nearest correlation matrix to the target matrix with the fixed correlations unaltered. However, the number of fixed correlations could be potentially very large, posing a computational challenge to existing methods. In this paper, we propose an unconstrained convex optimization approach by solving one or a sequence of continuously differentiable (but not twice continuously differentiable) convex optimization problems, depending on different stress patterns. This research fully takes advantage of the recently developed theory of strongly semismooth matrix valued functions, which makes fast convergent numerical methods applicable to the underlying unconstrained optimization problem. Promising numerical results on practical data (RiskMetrics database) and randomly generated problems of larger sizes are reported
stress testing, convex optimization, Newton’s method, augmented lagrangian functions
0926-6003
427-462
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Sun, Defang
31e918ef-960f-4304-8a2e-f1b8c6af1417
Qi, Houduo
e9789eb9-c2bc-4b63-9acb-c7e753cc9a85
Sun, Defang
31e918ef-960f-4304-8a2e-f1b8c6af1417

Qi, Houduo and Sun, Defang (2010) Correlation stress testing for value-at-risk: an unconstrained convex optimization approach. Computational Optimization and Applications, 45 (2), 427-462. (doi:10.1007/s10589-008-9231-4).

Record type: Article

Abstract

Correlation stress testing is employed in several financial models for determining the value-at-risk (VaR) of a financial institution’s portfolio. The possible lack of mathematical consistence in the target correlation matrix, which must be positive semidefinite, often causes breakdown of these models. The target matrix is obtained by fixing some of the correlations (often contained in blocks of submatrices) in the current correlation matrix while stressing the remaining to a certain level to reflect various stressing scenarios. The combination of fixing and stressing effects often leads to mathematical inconsistence of the target matrix. It is then naturally to find the nearest correlation matrix to the target matrix with the fixed correlations unaltered. However, the number of fixed correlations could be potentially very large, posing a computational challenge to existing methods. In this paper, we propose an unconstrained convex optimization approach by solving one or a sequence of continuously differentiable (but not twice continuously differentiable) convex optimization problems, depending on different stress patterns. This research fully takes advantage of the recently developed theory of strongly semismooth matrix valued functions, which makes fast convergent numerical methods applicable to the underlying unconstrained optimization problem. Promising numerical results on practical data (RiskMetrics database) and randomly generated problems of larger sizes are reported

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More information

Published date: March 2010
Keywords: stress testing, convex optimization, Newton’s method, augmented lagrangian functions
Organisations: Operational Research

Identifiers

Local EPrints ID: 54532
URI: http://eprints.soton.ac.uk/id/eprint/54532
ISSN: 0926-6003
PURE UUID: 3a972f53-d639-46c0-a8ee-243b7a89f015
ORCID for Houduo Qi: ORCID iD orcid.org/0000-0003-3481-4814

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Date deposited: 22 Mar 2010
Last modified: 16 Mar 2024 03:41

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Author: Houduo Qi ORCID iD
Author: Defang Sun

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