Operational–risk Dependencies and the Determination of Risk Capital

Abstract

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.Copula, Nonparametric Tail Dependence, Basel II, Loss Distribution Approach, Value–at–Risk, Subadditivity