Section 285 of the Solvency Regulation (as of 01.01.2007)

Correlations
¹Individual risk estimates for operational risks may be added when calculating the capital requirement for operational risk. ²But if correlations between individual risk estimates are recognised when calculating the capital requirement, the following requirements shall be met:

1. All correlation assumptions made when calculating the capital requirement for operational risk shall be plausible and substantiated.

2. The systems for determining correlations shall be sound and take uncertainties into account.

3. The institution shall validate its correlation assumptions using quantitative and qualitative techniques and if necessary adjust them.

Explanatory comments

On section 285:

In principle the term "correlations" used in the Solvency Ordinance, the Directive and the Basel II Framework includes all dependencies between the loss data included in the model¹.

In those cases in which the model is not based on a partitioned matrix this recommendation does not apply.

On sentence 1:

Individual risk estimates for operational risk may be added when calculating the capital requirement for operational risk. Irrespective of this, pursuant to section 284 (4) SolvV appropriate techniques must be used in developing a model for measuring operational risks and in validating the model, so that the individual risk estimates are determined in a way that justifies their summation. Losses that are attributable to the same event should as far as possible – and especially in the case of large loss events – be grouped together at the data preparation stage and included in the modelling as an aggregate loss event (collective loss).

On sentence 2:

With internal loss data, external data and scenario analyses a wide range of loss data are used in AMA modelling. These data are collected, further processed and aggregated in different ways in institution-specific AMA approaches; they are also given different weightings for the purposes of determining the capital requirement for operational risk. If an AMA model is based on a partitioned² matrix constructed on the basis of business lines and loss event categories as per Basel II and the EU Directive or on the basis of categories defined by the institution itself, correlations within the narrower meaning of the Solvency Ordinance refer to the dependencies between the different cells or groups of cells in this matrix. In this case the concept within the narrower meaning does not comprise the dependencies of data within a cell or group of cells, which are either assumed to be independent of each other or their dependencies may be taken into account through corresponding distribution families (e.g. negative binomial instead of Poisson). The correctness/plausibility of the assumptions made must be demonstrated by institutions accordingly.

For the purpose of determining and modelling correlations, various techniques may be used. In practice the correlations will be recognised in the model in different ways:

• Correlations of severities: Losses that are attributable to the same event should as far as possible – especially in the case of large loss events – be grouped together at the data preparation stage and included in the modelling as an aggregate loss event (collective loss). This represents a correlation of one, which must be taken into account in the model especially when pro rata use of collective losses is made.

• Correlation of frequency: The correlations are determined on the basis of the loss data or expert estimates consistent with the loss data. Depending on the technique selected, the resulting dependency model is applied to e.g. aggregate loss distributions or frequency of losses. Due account must be taken of any uncertainties by setting the parameters conservatively.

The correlation assumptions must be adequately substantiated and, as part of the institution's internal AMA model, documented. As long as adequate statistical substantiation of the correlation assumptions is not possible due to the small amount of data, other suitable qualitative and quantitative techniques may be used.

The correlations and correlation assumptions must be reviewed regularly over time by means of e.g. the loss data history, the results of new scenario analyses and new scientific findings. If deviations or uncertainties are identified during this review, due account should be taken of this by no later than the next scheduled modelling. A prompt re calculation will be necessary especially if a significant increase in the capital requirement is foreseeable.

¹Loss data do not include business environment and internal control factors, since they are frequently already included in the other items and are not independent loss-related data points.

²Broken down into groups of cells fully and with no overlaps.