Scaling Models for the Severity and Frequency of External Operational Loss Data

According to Basel II criteria, the use of external data is absolutely indispensable to the implementation of an advanced method for calculating operational capital. This article investigates how the severity and frequencies of external losses are scaled for integration with internal data. We set up an initial model designed to explain the loss severity. This model takes into account firm size, location, and business lines as well as risk types. It also shows how to calculate the internal loss equivalent to an external loss, which might occur in a given bank. OLS estimation results show that the above variables have significant power in explaining the loss amount. They are used to develop a normalization formula. A second model based on external data is developed to scale the frequency of losses over a given period. Two regression models are analyzed: the truncated Poisson model and the truncated negative binomial model. Variables estimating the size and geographical distribution of the banks' activities have been introduced as explanatory variables. The results show that the negative binomial distribution outperforms the Poisson distribution. The scaling is done by calculating the parameters of the selected distribution based on the estimated coefficients and the variables related to a given bank. Frequency of losses of more than $1 million are generated on a specific horizon.