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Volume 4/Number 4, Winter 2009/10 Research Papers Estimating operational risk capital for correlated, rare events Stefan Mittnik
Center for Quantitative Risk Analysis (CEQURA) and Department of Statistics, University of Munich, Akademiestrasse 1/I, 80799 Munich, Germany; email: finmetrics@stat.uni-muenchen.de and Center for Financial Studies, Frankfurt, Germany Tina Yener
Center for Quantitative Risk Analysis (CEQURA) and Department of Statistics, University of Munich, Akademiestrasse 1/I, 80799 Munich, Germany; email: tina.yener@stat.uni-muenchen.de We show that the use of conventional correlations for modeling dependencies may lead to counterintuitive behavior of risk measures such as value-at-risk and expected shortfall in simulation-based assessments of the risk of very rare events. The phenomenon can be avoided in the case of expected shortfall by an appropriate design of the simulation setup, but not for the widely used value-at-risk measure. Consequently, the goal of decreasing minimum capital requirements by specifying less-than-perfect correlations, as suggested by the New Basel Capital Accord (Basel II), may not be achieved.
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