Diversification effects in operational risk: A robust approach

Both the Basel II regulation for banks and the planned Solvency II directive for insurance companies allow institutions to reduce the operational risk capital in their internal model when they can demonstrate the existence of diversification effects. This paper shows how an institution can directly derive the dependency structure between operational risk cells from internal loss data in a realistic setting. Furthermore, it is demonstrated how the institution can, in a statistically sound manner, prove that the effect of diversification on the capital charge is taken into account in a conservative way. The presented approach should therefore allow an institution to reduce its overall operational risk capital due to diversification effects. As all parameters are derived from data already known to companies, using an operational risk model based on internal loss data (loss distribution approach), the concurrent implementation effort is relatively small. The derivation of correlation parameters is demonstrated using internal loss data from UniCredit Group. The resulting effect on the overall capital at risk is shown on the basis of a simplified loss distribution approach.