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

TL;DR

This paper introduces the Reduced-bias Capital Estimator (RCE), a novel method that significantly improves the accuracy, precision, and robustness of operational risk capital estimates under the Basel II/III framework, addressing bias caused by heavy-tailed loss distributions.

Contribution

The paper presents RCE, a new estimator that eliminates upward bias in high quantile VaR estimates, enhancing the reliability of operational risk capital calculations.

Findings

RCE reduces bias in capital estimates caused by heavy-tailed distributions.

RCE increases the precision and robustness of operational risk capital estimates.

Implementation of RCE is straightforward with standard statistical software.

Abstract

The largest US banks are required by regulatory mandate to estimate the operational risk capital they must hold using an Advanced Measurement Approach (AMA) as defined by the Basel II/III Accords. Most use the Loss Distribution Approach (LDA) which defines the aggregate loss distribution as the convolution of a frequency and a severity distribution representing the number and magnitude of losses, respectively. Estimated capital is a Value-at-Risk (99.9th percentile) estimate of this annual loss distribution. In practice, the severity distribution drives the capital estimate, which is essentially a very high quantile of the estimated severity distribution. Unfortunately, because the relevant severities are heavy-tailed AND the quantiles being estimated are so high, VaR always appears to be a convex function of the severity parameters, causing all widely-used estimators to generate biased capital estimates (apparently) due to Jensen's Inequality. The observed capital inflation is sometimes enormous, even at the unit-of-measure (UoM) level (even billions USD). Herein I present an estimator of capital that essentially eliminates this upward bias. The Reduced-bias Capital Estimator (RCE) is more consistent with the regulatory intent of the LDA framework than implementations that fail to mitigate this bias. RCE also notably increases the precision of the capital estimate and consistently increases its robustness to violations of the i.i.d. data presumption (which are endemic to operational risk loss event data). So with greater capital accuracy, precision, and robustness, RCE lowers capital requirements at both the UoM and enterprise levels, increases capital stability from quarter to quarter, ceteris paribus, and does both while more accurately and precisely reflecting regulatory intent. RCE is straightforward to implement using any major statistical software package.