Operational Risk Capital Models (2nd edition)
First published:
ISBN: 9781782724223
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Appendix 1: Credibility theory
Daniel Rodríguez
Appendix 1: Credibility theory
Introduction
Challenges of operational risk advanced capital models
Part I: Capture and Determination of the Four Data Elements
Collection of operational loss data: ILD and ED
Scenario analysis framework and BEICFs integration
Part II: General Framework for Operational Risk Capital Modelling
Loss data modelling: ILD and ED
Distributions for modelling operational risk capital
Scenario analysis modelling
Exposure-based approaches
BEICFs modelling and integration into the capital model
Hybrid model construction: Integration of ILD, ED and SA
Derivation of the joint distribution and capitalisation of operational risk
Backtesting, stress testing and sensitivity analysis
Regulatory approval report
Evolving from a plain vanilla to a state-of-the-art model
Part III: Use Test, Integrating Capital Results into the Institution’s Day-to-day Risk Management
Strategic and operational business planning and monitoring
Risk/reward evaluation of mitigation and control effectiveness
Appendix 1: Credibility theory
Appendix 2: Mathematical optimisation methods required for operational risk modelling and other risk mitigation processes
Business risk quantification
This appendix introduces the different models of credibility theory: classical model, Buhlmann, Buhlmann–Straub, and Buhlmann–Straub for small and large losses.
CLASSICAL CREDIBILITY MODELS
This section presents the classical credibility model. Classical credibility has the disadvantage of requiring the underlying data to be normally distributed, which is uncommon for operational risk losses. Nevertheless, it is presented for its simplicity to facilitate the understanding of all other credibility models.
Classical probability theory (also known as limited-fluctuation credibility) starts with two estimations obtained from different sources, denoted as estimates x and y. Each of these estimates has a specific variance, denoted as σx2 for x and σy2 for y. Estimate x, which generally refers to the institution´s internal loss data (ILD), is associated with a weight-named credibility factor and denoted by z, which will be between zero and one. The mean value of both estimates can be obtained by the expression:
| (A1.1) |
This equation shows that the value of is between x and y values. The credibility factor, z, indicates the relative
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