On Stability of Operational Risk Estimates by LDA: From Causes to Approaches

Abstract

The stability of estimates is critical when applying advanced measurement approaches (AMA) such as loss distribution approach (LDA) for operational risk capital modeling. Recent studies have identified issues associated with capital estimates by applying the maximum likelihood estimation (MLE) method for truncated distributions: significant upward mean-bias, considerable uncertainty about the estimates, and non-robustness to both small and large losses. Although alternative estimation approaches have been proposed, there has not been any comprehensive review of the causes of instability and how the alternative approaches either address the sources of instability or improve estimates compared to the MLE method. In this paper, we systematically review the causes of capital instability. Then we review several approaches (right-truncated distributions, bias-corrected capital estimators and quantile-distance estimation) in addressing each source of instability. First, we analyze the advantages of imposing an upper bound on a single loss in order to address the infinite-mean issue and make the subjective assumptions (if necessary) understandable for risk managers and regulators. We also provide a framework for calculating the expected loss and for approximating capital estimates under the right-truncation formulation. Second, we summarize performance measures for evaluating capital estimates and provide a simulation-based approach to correct the bias of capital estimates when MLE is employed. In doing so, we point out that although the approach may decrease the mean-bias, it introduces more median-bias. Finally, while noting the potential robustness of applying the quantile-distance estimator, we review the factors that affect the capital estimator’s performance, and suggest that this method should be used with caution because of its significant sensitivity to various definitions of quantile distance.