Estimating Operational Risk Capital with Greater Accuracy, Precision, and Robustness

• Activity Number: 341
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Risk Analysis
• Author(s): John Opdyke*+
• Companies: GE Capital
• Keywords: Operational Risk ; Basel II ; Jensen's Inequality ; Economic Capital ; Regulatory Capital ; Severity Distribution

Abstract

The Loss Distribution Approach (LDA) has become the industry standard for the largest US banks to estimate the operational risk capital they must hold per regulatory mandate (a la Basel II). LDA defines the aggregate loss distribution as the convolution of the estimated loss frequency and loss severity distributions, and estimated capital is the Value-at-Risk (99.9%tile) of this annual loss distribution. However, for all the relevant severities, VaR always appears to be a convex function of the distributions' parameter vectors because they all are heavy-tailed AND the VaR being estimated corresponds to such an extremely high severity quantile. Therefore, due to Jensen's inequality estimated capital always will be inflated, and this bias sometimes can be enormous (billions $). Herein I present an estimator of capital that dramatically reduces this systematically upward bias when used with any commonly used estimator of the severity parameters. The reduced-bias capital estimator (RCE) also notably increases the precision of the capital estimate, as well as its robustness to violations of the i.i.d. presumption. RCE is straightforward to implement using any major statistical package.