Combining scenario and historical data in the loss distribution approach: A new procedure that incorporates measures of agreement between scenarios and historical data. PJ de Jongh 1 , T de Wet 2 , H Raubenheimer 3 and JH Venter 4 Abstract Many banks use the loss distribution approach in their advanced measurement models to estimate regulatory or economic capital. This boils down to estimating the 99.9% VaR of the aggregate loss distribution and is notoriously difficult to do accurately. Also, it is well-known that the accuracy with which the tail of the loss severity distribution is estimated is the most important driver in determining a reasonable estimate of regulatory capital. To this end, banks use internal data and external data (jointly referred to as historical data) as well as scenario assessments in their endeavour to improve the accuracy with which the severity distribution is estimated. In this paper we propose a simple new method whereby the severity distribution may be estimated using historical data and experts’ scenario assessments jointly. The way in which historical data and scenario assessments are integrated incorporates measures of agreement between these data sources, which can be used to evaluate the quality of both. In particular we show that the procedure has definite advantages over traditional methods where the severity distribution is modelled and fitted separately for the body and tail parts, with the body part based only on historical data and the tail part on scenario assessments. 1 Introduction Many banks worldwide currently use various versions of the so-called loss distribution approach (LDA) to calculate Value-at-Risk (VaR) for Operational Risk under the Basel Accord’s Advanced Measurement Approach (AMA). For a description of the practical application of the LDA in a bank the interested reader is referred to Aue and Kalkbrener (2007). 1 Director of the Centre for Business Mathematics and Informatics (BMI), North-West University (NWU). 2 Extra-ordinary professor at the Centre for BMI, NWU 3 Associate professor at the Centre for BMI, NWU. 4 Professor at the Centre for BMI, NWU. 1