Operational Risk Capital Models (2nd edition)
First published:
ISBN: 9781782724223
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Distributions for modelling operational risk capital
Daniel Rodríguez
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
Probability distributions (French and Insua, 2000) play a role in the operational risk modelling process that permits us to interpolate and extrapolate from the observed loss sample. Indeed, in capital modelling, the capital charge is determined through probability distributions. The number of times an operational event takes place is determined by a discrete probability distribution, such as a Poisson or a negative binomial. On the other hand, the loss amount for any of the events is determined by a continuous positive probability distribution, such as gamma, lognormal or Pareto distributions. These examples are parametric distributions, where a mathematical expression and a set of parameters completely define the probability of all attainable values. It is also possible to define distributions using empirical data, mixing two or more parametric distributions or changing the range in which the distributions are defined by means of its truncation or shifting.
Mathematically, a probability distribution is a function that describes all the possible values and likelihoods that a random variable can take within a given range. This relationship can be expressed by different
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