Formulating hypothetical scenarios in correlation stress testing via a Bayesian framework

• Published in: The North American journal of economics and finance Vol. 27; pp. 17 - 33
• Main Authors: Yu, Philip L.H., Li, W.K., Ng, F.C.
• Format: Journal Article
• Language: English
• Published: Greenwich Elsevier Inc 01.01.2014; Elsevier Science Ltd
• Subjects: Algorithms; Bayesian analysis; Bayesian estimation; Block Gibbs sampling; Computer simulation; Correlation analysis; Correlation stress testing; Economic crisis; Scenario test; Studies; Bayesian estimation; Correlation stress testing; Block Gibbs sampling; Scenario test
• ISSN: 1062-9408; 1879-0860
• DOI: 10.1016/j.najef.2013.10.002

•We model the correlation matrix under hypothetical scenarios in stress testing.•Predict the values of other correlations given adjustments on some correlations.•Our empirical example shows that empirical correlations are correlated.•Including correlations among empirical correlations yields a more realistic result.•Extend the posterior simulation algorithm to update two correlations simultaneously. Correlation stress testing refers to the correlation matrix adjustment to evaluate potential impact of the changes in correlations under financial crises. There are two categories, sensitivity tests and scenario tests. For a scenario test, the correlation matrix is adjusted to mimic the situation under an underlying stress event. It is only natural that when some correlations are altered, the other correlations (peripheral correlations) should vary as well. However, most existing methods ignore this potential change in peripheral correlations. In this paper, we propose a Bayesian correlation adjustment method to give a new correlation matrix for a scenario test based on the original correlation matrix and views on correlations such that peripheral correlations are altered according to the dependence structure of empirical correlations. The algorithm of posterior simulation is also extended so that two correlations can be updated in one Gibbs sampler step. This greatly enhances the rate of convergence. The proposed method is applied to an international stock portfolio dataset.