Discussion Paper Series 2015-E-1

Risk Aggregation with Copula for Banking Industry

Toshinao Yoshiba

This paper surveys several applications of parametric copulas to market portfolios, credit portfolios, and enterprise risk management in the banking industry, focusing on how to capture stressed conditions. First, we show two simple applications for market portfolios: correlation structures for returns on three stock indices and a risk aggregation for a stock and bond portfolio. Second, we show two simple applications for credit portfolios: credit portfolio risk measurement in the banking industry and the application of copulas to CDO valuation, emphasizing the similarity to their application to market portfolios. In this way, we demonstrate the importance of capturing stressed conditions. Finally, we introduce practical applications to enterprise risk management for advanced banks and certain problems that remain open at this time.

Keywords: copula; multivariate distribution; tail dependence; risk aggregation; economic capital

Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.

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