Estimating operational risk capital with greater accuracy, precision and robustness

Abstract

The largest US banks and Systemically Important Financial Institutions 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 of these institutions use the Loss Distribution Approach (LDA) which defines the aggregate loss distribution as the convolution of a frequency distribution and a severity distribution representing the number and magnitude of losses, respectively. Capital is a Value-at-Risk estimate of this annual loss distribution (i.e. the quantile corresponding to the 99.9%tile, representing a one-in-a-thousand-year loss, on average). In practice, the severity distribution drives the capital estimate, which is essentially a very large quantile of the estimated severity distribution. Unfortunately, when using LDA with any of the widely used severity distributions (i.e. heavy-tailed, skewed distributions), all unbiased estimators of severity distribution parameters appear to generate biased capital estimates due to Jensen's Inequality: VaR always appears to be a convex function of these severities' parameter estimates because the (severity) quantile being estimated is so large and the severities are heavy-tailed. The resulting bias means that capital requirements always will be overstated, and this inflation is sometimes enormous (sometimes even billions of dollars at the unit-of-measure level). Herein I present an estimator of capital that essentially eliminates this upward bias when used with any commonly used severity parameter estimator. The Reduced-bias Capital Estimator (RCE), consequently, is more consistent with regulatory intent regarding the responsible implementation of the LDA framework than other implementations that fail to mitigate, if not eliminate 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 unit-of-measure 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 explain, understand, and implement using any major statistical software package.

Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2014 Update

“…The measurements of operational risks and the corresponding management instruments are the focuses of operational risk research. Dutta and Babbel () promote the scenario analysis approach, and Opdyke () develops the reduced‐bias capital estimator to measure operational risks.…”

Model Uncertainty in Operational Risk Modeling Due to Data Truncation: A Single Risk Case

“…This implies that any quantile of the observable variable X is never below the corresponding quantile of the unobservable variable Y, which is true VaR. This fact is certainly not new (for example, see the extensive analysis by Opdyke (2014), about the effect of Jensen's inequality in VaR estimation). However, if we now change our perspective from mathematical to statistical and take into account the method of how VaR is estimated, we could augment the above discussion with new insights and improve our understanding.…”

“…7.9). Furthermore, as is known in practice, the severity distribution is a key driver of the capital estimate (Opdyke 2014). This is the part of the aggregate model where initial assumptions about the data collection threshold are most influential.…”

Operational Risk Management in Financial Institutions: A Literature Review

“…The second largest topic (with 79 articles) is the "Application" of different models on the systematically collected internal or external operational loss databases (see, for instance, [5,[35][36][37][38][39][40][41][42][43][44]). Studies that apply their models using simulated data are excluded from this subcategory and are part of the first subcategory and include, for instance, [45][46][47][48][49][50].…”