**6. Some further practical considerations**

*Data Scaling.* It is practice in operational risk management to use different data sources for modelling future losses. Banks have been collecting their own data, but realistically, most banks only have between five and ten years of reliable loss data. To address this shortcoming, loss data from external sources can be used by banks in addition to their own internal loss data and controls. External loss data comprises operational risk losses experienced by third parties, including publicly available data, insurance data and consortium data. [16] investigate whether the size of operational risk losses is correlated with geographical region and firm size. They use a quantile matching algorithm to address statistical issues that arise when estimating loss scaling models when subjecting the data to a loss reporting threshold. [13] uses regression analysis based on the GAMLSS (generalised additive models for location scale and shape) framework to model the scaling properties. The severity of operational losses using the extreme value theory is used to account for the reporting bias of the external data losses.

*No historical data available*. In the event of having insufficient historical data available, the GPD approach as discussed above may be used. *Te*ð Þ *x* in (2) can be estimated by a right truncated distribution, e.g. scaled beta, Pareto type II, etc. fitted to an expected loss scenario and *q*7. In this case the expert should also provide a scenario for the expected loss *EL* ¼ *E T*j*X* ≤*q*<sup>7</sup> . *Tu*ð Þ *<sup>x</sup>* can be estimated by a GPD distribution as discussed in the GPD approach.

*Aggregation*. To capture dependencies of potential operational risk losses across business lines or event types, the notion of copulas may be used (see [15]). Such dependencies may result from business cycles, bank-specific factors, or crossdependence of large events. Banks employing more granular modelling approaches may incorporate a dependence structure, using copulas to aggregate operational risk losses across business lines and/or event types for which separate operational risk models are used.

*Construction of Forward-Looking Distributions Using Limited Historical Data and Scenario… DOI: http://dx.doi.org/10.5772/intechopen.93722*
