Operational Risk Capital Models (2nd edition)
First published:
ISBN: 9781782724223
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Appendix 2: Mathematical optimisation methods required for operational risk modelling and other risk mitigation processes
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
Mathematical optimisation has significant applications in risk measurement and mitigation. In particular, it is used in operational risk modelling for the determination of the severity and frequency distribution functions that best represent the operational risk profile of the institution.
Additionally, mathematical optimisation has other applications in risk management, such as the selection of portfolios of risk exposures (market and credit risk) consistent with risk-averse strategies (Escudero et al, 2014). In fact, the choice of risk exposures can also be applied to operational risk such as in the selection of the optimal insurance programmes for the hedging of operational risk exposures (see Chapter 15).
In this appendix, we present optimisation algorithms for the operational risk distribution function determination. Additionally, we introduce examples of how to implement mathematical optimisation into portfolio selection, in this case the optimisation of credit exposures to obtain a desired risk profile consistent with risk-averse strategies.
MATHEMATICAL OPTIMISATION METHODS FOR OPERATIONAL RISK MEASUREMENT
The process for determining the optimal distribution
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