Operational Risk Capital Estimation and Planning: Exact Sensitivity Analysis and Business Decision Making Using the Influence Function

Abstract

Financial institutions have invested tremendous resources to develop operational risk capital models within the framework of the Advanced Measurement Approach (AMA) of the Basel II Accord. Most of this effort has focused on satisfying evolving regulatory requirements in the near term rather than risk-conscious business decision making in the long term. However, a critical objective of the Basel II Accord is to move institutions beyond viewing operational risk capital modeling as a mere regulatory exercise to embedding operational risk awareness into risk-informed decision making throughout the institution. To this end, we illustrate in this chapter the use of the Influence Function as a powerful analytical tool that allows the operational risk practitioner to leverage existing AMA models to generate critical quantitative insights for direct business decision-making by users of operational risk capital estimates.

Borrowed from the robust statistics literature, the Influence Function (IF) is an extremely useful and relevant methodology that provides a theoretical basis for capital planning and business decision making via exact sensitivity analysis. Because it is based on analytic derivations, the IF avoids the need to perform often resource-intensive, arguably subjective, and often inconclusive or inaccurate simulations. We clearly demonstrate how the IF utilizes any given estimator of the severity model (easily the main driver of estimated capital requirements), the values of its parameter estimates, and an assumed forward looking frequency to define Exact Sensitivity Curves for Regulatory Capital and Economic Capital. These curves can be used to conduct exact sensitivity analyses on the capital impacts of hypothetical changes to the underlying loss data. Hypothetical loss scenarios of interest to bank management may be current or prospective, such as assessing the potential capital impact of a single hypothetical “tail” event of differing magnitudes. Relevant loss scenarios also may be retrospective, providing “but for” and exact attribution analyses as to why capital changed from one quarter to another. The information generated from these sensitivity analyses can suggest potential enhancements to the estimation of severity model parameters, and more broadly, better inform decision-making based on a more precisely defined risk profile.

Keywords: Robust Statistics, Severity, Capital Estimation, Influence Function, Sensitivity Analysis, OBRE, MLE, Basel II

JEL Classification: C02, G21, G32