Combining Scenario and Historical Data in the Loss Distribution Approach: A New Procedure that Incorporates Measures of Agreement between Scenarios and Historical Data

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% value-at-risk 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 endeavor to improve the accuracy with which they estimate the severity distribution. In this paper, we propose a simple new method whereby the severity distribution may be estimated using both historical data and experts' scenario assessments. 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 in which the severity distribution is modeled and fitted separately for the body and tail parts, with the body part based only on historical data and the tail part based on scenario assessments.

Keywords: loss distribution approach, severity distribution estimation, aggregate loss distribution estimation, combining historical data with scenario information, measures of agreement