Advanced operational risk modelling for banks and insurance companies

The aim of this paper is to measure operational risk in financial institutions when historical data are available starting from a fixed threshold. To quantify the operational risk we apply the Loss Distribution Approach (LDA), a frequency/severity approach widely used in the actuarial models. Risk measures like Value at Risk (VaR) and Expected Shortfall (ES) are used for determining the risk capital necessary to cover the operational risk. The dependence among the events in the operational risk management has been taken into account using copula functions. We employed for this purpose the Student copula, which is widely used in financial modelling. Extreme Value Theory (EVT) has been used to model the right tail of the severity of loss distributions. The Expectation and Maximization (EM) algorithm has been applied to estimate the parameters of the frequency and severity of loss distributions when only their left truncated distributions are available. We conclude then with a numerical application of the proposed model which aims at evaluating the risk capital for a single financial institution. To this scope we have used, as empirical observations, the OpData® dataset supplied by OpVantage®. In order to estimate the risk capital, we calculate the Value at Risk of the simulated operational loss distribution.