Estimating the correlation between operational risk loss categories over different time horizons

Operational risk is challenging to quantify because of the broad range of categories it encompasses (eg, fraud, technological issues, natural disasters) and the heavy-tailed nature of realized losses. Operational risk modeling requires quantifying how these broad loss categories are related. We focus on the issue of loss frequencies having different timescales (eg, daily, monthly or yearly) and, in particular, on estimating the statistics of losses over arbitrary time horizons. We present a frequency model whereby mathematical techniques can feasibly be applied to analytically calculate means, variances and covariances that are more accurate than those achieved by time-consuming Monte Carlo simulations. We show that the analytic calculations of cumulative loss statistics in an arbitrary time window, which would otherwise be intractable due to temporal correlations, are feasible under our model. Our work has potential value because these statistics are crucial for approximating correlations of losses via copulas. We systematically vary all model parameters to demonstrate the accuracy of our methods for calculating all first- and second-order statistics of aggregate loss distributions. Finally, using combined data from a consortium of institutions, we show that different time horizons can lead to a wide range of loss statistics that can significantly affect calculations of capital requirements.