Operational–risk dependencies and the determination of risk capital

With the advent of Basel II, risk–capital provisions need to also account for operational
risk. The specification of dependence structures and the assessment of their effects
on aggregate risk–capital are still open issues in modeling operational risk. In this
paper, we investigate the potential consequences of adopting the restrictive Basel’s
Loss Distribution Approach (LDA), as compared to strategies that take dependencies
explicitly into account. Drawing on a real–world database, we fit alternative dependence
structures, using parametric copulas and nonparametric tail–dependence coefficients,
and discuss the implications on the estimation of aggregate risk capital.
We find that risk–capital estimates may increase relative to that derived for the
LDA when accounting explicitly for the presence of dependencies. This phenomenon
is not only be due to the (fitted) characteristics of the data, but also arise from the
specific Monte Carlo setup in simulation–based risk–capital analysis