Operational Risk - The Sting is Still in the Tail But the Poison Depends on the Dose

Abstract

This paper investigates the generalized parametric measurement methods of aggregate operational risk in compliance with the regulatory capital standards for operational risk in the New Basel Capital Accord ("Basel II"). Operational risk is commonly defined as the risk of loss resulting from inadequate or failed internal processes and information systems, from misconduct by people or from unforeseen external events. Our analysis informs an integrated assessment of the quantification of operational risk exposure and the consistency of current capital rules on operational risk. Given the heavy-tailed nature of operational risk losses, we employ extreme value theory (EVT) and the g-and-h distribution within a "full data" approach to derive point estimates of a unexpected operational risk at the 99.9th percentile in line with the Advanced Measurement Approaches (AMA). Although such internal risk estimates substantiate a close analytical representation of operational risk exposure, the accuracy and order of magnitude of point estimates vary greatly by percentile level, estimation method, and threshold selection. Since the scarcity of historical loss data defies back-testing at high percentile levels and requires the selection of extremes beyond a threshold level around the desired level of statistical confidence, the quantitative criteria of AMA standards appear overly stringent. A marginally lower regulatory percentile of 99.7% would entail an outsized reduction of the optimal loss threshold and unexpected loss at disproportionately smaller estimation uncertainty.

Keywords: operational risk, risk management, financial regulation, Basel Committee, Basel II, New Basel Capital Accord, extreme value theory, generalized extreme value (GEV) distribution, extreme value theory (EVT), generalized Pareto distribution (GPD), peak-over-threshold (POT) method, g-and-h distribution

JEL Classification: G10, G20, G21, D81