Capital Requirements to Cover Operational Risk in Financial Institutions of Emerging Markets. A Gaussian Copula Model

Context: Advanced Measurement Approach (AMA) has been the umbrella to identify the models used for modeling the capital to cover Operational Risk (Total Operational Value at Risk, OpVaR) in financial institutions in developed countries. The Loss Distribution Approach (LDA) has been the most popular model used by international banks for OpVaR calculation. However, the operational losses frequently have multivariate dependences that are not accounted for in the LDA. This paper applies a Gaussian copula to model the multivariate dependences in operational losses. Method: Two models were compared to estimate capital requirement for operational risk. Model (i) is the standard LDA model (BCBS 2004). Model (ii) incorporates a multivariate Gaussian copula into the LDA to model multivariate dependence between operational losses (severities). This research analyzes an operational loss data set, SAS® Operational Risk Global Data (SAS OpRisk Global Data), in order to model operational risk at financial institutions in emerging markets between 1990 and 2013. Results: The impact of Model (ii) was evaluated on the estimates of the total regulatory capital for operational risk and compared with the one predicted by (i). The results confirm the existence of diversification benefit up to 33%. Conclusions: Modeling explicitly the multivariate dependence between operational losses has a clear impact on capital requirement for institutions in emerging markets. The implementation of a Gaussian copula into the LDA model provides a sophisticated tool to estimate operational risk capital in emerging markets, as well as the possibility for diversification benefit. Acknowledgements: To SAS for providing the database used in this research.