Jun 10

Operational loss dependencies (Academic Paper)

by David Harper, CFA, FRM, CIPM

FRM |

Ganna Reshetar gives a brief, helpful introduction to the loss distribution approach (LDA) under Basel II. Basel II does not give a bank credit (diversification benefits) for imperfect correlations among operational losses, either among loss types or across business lines. The paper explores the use of a mixture distribution model to account for dependencies (correlations); this would be invalid under Basel II but is still instructive. Another way to view the Basel approach is: the implicit assumption of perfect correlation is an extreme conservatism.

Basel II allow for three approaches to operational risk:

  1. Basic Indicator Approach (BIA),
  2. Standardized Approach (SA). BIA and SA use gross income as gauges of operational risk. Pretty rough. Or, the more sophisticated…
  3. Advanced Measurement Approach (AMA). Under AMA, banks may choose LDA or another internal operational risk measurement model developed by a bank

In Basel, operational losses fall into 56 (8 x 7) risk classes: losses are classified among seven loss types (Internal Fraud; External Fraud; Employment Practices and Workplace Safety; Clients, Products and Business Practices; Damage to Physical Assets; Business Disruption and System Failure; and Execution, Delivery and Process Management) and eight business lines (Corporate Finance; Trading and Sales; Retail Banking; Payment and Settlement; Agency Services; Commercial Banking; Asset Management; and Retail Brokerage)

Implementation of LDA under Basel II involves five steps:

  1. Model severity of loss events (typically continuous; e.g., Pareto distribution)
  2. Model frequency of loss events (discrete; e.g., negative binomial, Poisson)
  3. Estimate the compound operational loss distribution (the LDA). "In general, there is no analytical expression of the compound loss distribution. Computing this distribution requires numerical algorithms such as the Monte Carlo method …"
  4. Use the compound (LDA) distribution to obtain the Capital at Risk (CaR) for each class of risk. Basel's CaR is the operational VaR for a one-year holding period and a 99.9% confidence level.
  5. Sum all capital charges across all classes of risk; i.e., no credit for dependence/diversification 

However, the author uses a mixture model to capture three types of operational dependencies:

  • Dependence between loss severities. "We may observe that historically, the loss amounts are high (or low) in one business line of a bank when the loss amounts are high (or low) in another business line of a bank. This can be explained by the fact that severities of losses in both business lines are dependent because they are driven by the same factor (macroeconomic, political, internal for a bank etc.)."
  • Dependence between loss frequencies. Similar logic.
  • Dependence between risk classes (e.g., internal fraud and employee practices). "After aggregation of losses on the level of a class of risk we obtained a third type of loss dependence, which is dependence between risk classes, and which is driven by the underlying frequency and severity dependencies."

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