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.Operational risk in banks, scaling, severity distribution, frequency distribution, truncated count data regression models

Extremal Events in a Bank Operational Losses

Operational losses are true dangers for banks since their maximal values to signal default are difficult to predict. This risky situation is unlike default risk whose maximum values are limited by the amount of credit granted. For example, our data from a very large US bank show that this bank could suffer, on average, more than four major losses a year. This bank had seven losses exceeding hundreds of millions of dollars over its 52 documented losses of more than $1 million during the 1994-2004 period. The tail of the loss distribution (a Pareto distribution without expectation whose characteristic exponent is 0.95 ? ? ? 1) shows that this bank can fear extreme operational losses ranging from$1 billion to $11 billion, at probabilities situated respectively between 1$350 M and close to $1 billion.Bank operational loss, value at risk, Pareto distribution, insurance premium, extremal event

Scaling models for the severity and frequency of external operational loss data

According to Basel II criteria, the use of external data is indispensable to the implementation of an advanced method for calculating operational risk 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 by taking into account potential selection bias in the external data. Estimation results show that many variables have significant power in explaining the loss amount. We use them to develop a normalization formula. We develop a zero-inflated count-data model to scale the loss frequency. We compute an operational VaR and we conduct out-of-sample backtesting.Operational risk in banks External operational losses Frequency distribution Zero-inflated count-data models Selection model