Internal Data, External Data and Consortium Data - How to Mix Them for Measuring Operational Risk

It is widely recognized that calibration on internal data may not suffice for computing an accurate capital charge against operational risk. However, pooling external and internal data lead to unacceptable capital charges as external data are generally skewed toward large losses. In a previous paper, we have developped a statistical methodology to ensure that merging both internal and external data leads to unbiased estimates of the loss distribution. This paper shows that this methodology is applicable in real - life risk management and that it permits to pool internal and external data together in an appropriate way. The paper is organized as follows. We first discuss how external databases are designed and how their design may result in statistical flaws. Then we develop a model for the data generating process which underlies external data. In this model, the bias comes simply from the fact that external data are truncated above a specific threshold while this threshold may be either constant but known, or constant but unknown, or finally stochastic. We describe the rationale behind these three cases and we provide for each of them a methodology to circumvent the related bias. In each case, numerical simulations and practical evidences are given