EBA欧洲银行-B1-Kerbl-Evidence2C20Estimates-and-Extreme-Values-from-Austria_24页_685kb

Summary of "Operational Risk: Evidence, Estimates and Extreme Values from Austria"

Core Content

This paper presents an analysis of operational risk data from Austrian banks, focusing on the severity distribution of losses and the effectiveness of different statistical models in capturing these distributions. The study highlights the challenges in operational risk quantification due to the lack of comprehensive data and the tendency for analysts to rely on crude measures, such as assuming a proportional relationship between annual gross income and operational losses.

The research utilizes a rich data source, the Austrian Loss Data Collection, which includes more than 42,000 loss events reported by 167 banking entities. The data covers various business lines (BLs) and event types (ETs), with loss amounts rounded to the nearest thousand euros.

Main Research Questions

• What are the best parametric distributions for modeling operational loss severity?
• What are the statistical characteristics of different event types and business lines?
• How do the frequency and severity of operational losses relate to financial indicators?

Key Findings

Data Overview

• The data spans from 2007 to 2012.
• The most frequent event type is external fraud, with payment & settlement being the business line with the highest number of loss events.
• The mean loss for payment & settlement is significantly lower than the maximum loss, indicating the presence of extreme values in the data.
• The distribution of losses is highly skewed, with the mean loss lying beyond the 90% quantile.

Density Plots

• The uncapped density plots show an "L"-shaped distribution, indicating a heavy tail.
• When capped, the density becomes more right-skewed, suggesting that the extreme values are not captured well by simple models.

Cross-Section Analysis

• The frequency of losses is found to be highly dependent on bank variables.
• Operational Risk RWA (Risk-Weighted Assets) performs well in capturing both the frequency and total loss amount.
• Mean losses show negative linear correlation with financial indicators, but positive rank correlation, indicating that outliers have a significant impact.

Parametric Distributions

• The generalized Pareto distribution (GPD) is considered the best performer in most cases, with only one exception (retail brokerage) where it does not rank among the top two.
• The g- and h-distribution and lognormal distribution also perform well, particularly the lognormal which is surprisingly effective.
• The exponential distribution is the worst performer, confirming prior research that it is not suitable for modeling operational risk severity, especially in the tail.

Cross Validation Results

• The cross validation exercise involved 5000 iterations, randomly splitting the data into training and validation sets.
• The mean rank of the GPD varies across categories, with higher ranks observed in categories with fewer observations.
• For some business lines and event types, the GPD yields a parameter $\hat{\xi}$ > 1, which implies infinite mean and variance, highlighting the extreme nature of the data in these categories.

Conclusions

• Operational risk severity is highly heterogeneous across business lines and event types.
• Operational Risk RWA is the best indicator for both frequency and total loss amount.
• The GPD is effectively capturing the tail behavior of operational losses, with good performance in most categories.
• The relative performance of the GPD is strongly influenced by the number of observations, with fewer observations leading to poorer performance.
• The lognormal distribution performs surprisingly well, suggesting it may be a viable alternative to more complex models in certain contexts.