The mutual-information-based variance–covariance approach: an application to operational risk aggregation in Chinese banking

• Published in: Journal of operational risk 2014-09, Vol.9 (3), p.3-19
• Main Authors: Li, Jianping, Zhu, Xiaoqian, Xie, Yongjia, Chen, Jianming, Gao, Lijun, Feng, Jichuang, Shi, Wujiang
• Format: Article
• Language: English
• Subjects: Banking; Banking industry; Capital requirements; Comparative analysis; Correlation analysis; Datasets; Entropy; Lattice theory; Probability distribution; Random variables; Risk management; Studies
• ISSN: 1744-6740; 1755-2710; 1744-6740
• DOI: 10.21314/JOP.2014.140

Most advanced measurement approaches cannot simultaneously capture the overall dependence between operational risk components and be easy to use and understand. This paper proposes a mutual-information-based variance-covariance approach that is able to capture the overall correlation and is also highly tractable. Specifically, we replace the linear correlation coefficient with the global correlation coefficient in the framework of the variance-covariance approach. Originating from the theory of mutual information, the global correlation coefficient is able to capture both linear and nonlinear correlation relationships. The value-at-risk (VaR) of each individual risk component is calculated; these VaRs are then aggregated by using the global correlation coefficient. In empirical analysis, the proposed approach is employed to aggregate the operational risk of Chinese banking across business lines, based on the most comprehensive (to the best of our knowledge) operational risk data set. After an overall comparison with results from other correlation assumptions and the actual capital allocation of Chinese banking in 2013, we conclude that the actual capital allocation in China at present is not effective, and the aggregate VaR calculated from our approach is more reasonable.