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

50 Pages Posted: 30 Aug 2014 Last revised: 21 Feb 2017

See all articles by Xiaoping Zhou

Xiaoping Zhou

Citizens Financial Group; State University of New York (SUNY) - Department of Applied Mathematics and Statistics

Antonina Durfee

Citizens Financial Group

Frank J. Fabozzi

EDHEC Business School

Date Written: August 24, 2014

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.

Keywords: operational risk, capital modeling, stability of estimates, robust estimation, right-truncated distributions, bias corrected capital estimators, maximum likelihood estimation, quantile-distance estimators

Suggested Citation

Zhou, Xiaoping and Durfee, Antonina and Fabozzi, Frank J., On Stability of Operational Risk Estimates by LDA: From Causes to Approaches (August 24, 2014). Available at SSRN: https://ssrn.com/abstract=2486279 or http://dx.doi.org/10.2139/ssrn.2486279

Xiaoping Zhou (Contact Author)

Citizens Financial Group ( email )

28 State St
Boston, MA 02109
United States

State University of New York (SUNY) - Department of Applied Mathematics and Statistics ( email )

Stony Brook University
Stony Brook, NY 11794
United States

Antonina Durfee

Citizens Financial Group ( email )

28 State St
Boston, MA 02109
United States

Frank J. Fabozzi

EDHEC Business School ( email )

France
215 598-8924 (Phone)

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
148
Abstract Views
836
rank
172,347
PlumX Metrics