This chapter provides a detailed Overview of OpRisk methods to combine data sources, particularly aimed to aid practitioners in forming rigorous and statistically justified methods for combining different data sources. We cover in this chapter:
- Linear Weighted Combining based on the minimum variance principle;
- Bayesian methods for the combining of two data sources with posterior and predictive distributional models developed for frequency and severity models. Special topics include different methods for prior development and hyper-parameter estimation;
- Bayesian methods for combining expert opinion with internal and external data;
- Combining data sources using Linear Bayes or Credibility Theory;
- Non-parametric Bayesian methods for combining of data sources;
- Combining data sources based on other generalized uncertainty methods such as Dempster-Shafer theory and p-boxes.
It is hard to perform a robust estimation of low frequency/ high severity risks using data from a single financial institution. As the number of these large events in a financial institution would be minimal, any statistical analysis would present significant challenges. There is simply not enough data to estimate high quantiles of the risk distribution. Other sources of information that can be used to improve risk estimates and are required by the Basel II for OpRisk Advanced Measurement Approaches (AMA) are internal data, relevant external data, scenario analysis, ...