In this paper we study copula-based models for aggregation of operational
risk capital across business lines in a bank. A commonly used method of
summation of the value-at-risk (VaR) measures, that relies on a hypothesis
of full correlation of losses, becomes inappropriate in the presence of
dependence between business lines and may lead to over-estimation of the
capital charge. The problem can be further aggravated by the persistence
of heavy tails in operational loss data; in some cases, the subadditivity
property of value-at-risk may fail and the capital charge becomes underestimated.
We use a-stable heavy-tailed distributions to model the loss
data and then apply the copula approach in which the marginal
distributions are consolidated in the symmetric and skewed Student tcopula
framework. In our empirical study, we compare VaR and
conditional VaR estimates with those obtained under the full correlation
assumption. Our results demonstrate significant reduction in capita