Risk measurement, quantification and modelling
What the exam tests
Quantification: choosing measures, building and validating models, and communicating uncertainty. Expect calculations and critique of model assumptions.
Core rules
- Frequency-severity models combine a count distribution (Poisson, negative binomial) with a severity distribution (lognormal, Pareto, empirical).
- VaR is a quantile, not a maximum loss; TVaR/expected shortfall averages losses beyond the VaR threshold and is more sensitive to tail shape.
- Dependence matters: copulas, correlation matrices or scenario dependence change aggregate capital; diversification is not free.
- Validate with backtesting, sensitivity analysis, expert review and independent model validation; document data limitations and parameter uncertainty.
- Stress and scenario tests complement stochastic models, especially where data are sparse.
Worked example
Annual operational losses are modelled as Poisson(4) events with mean severity £50,000. Expected annual loss = 4 × £50,000 = £200,000. A simulation gives 99.5% VaR of £1.2m and TVaR of £1.9m. Reasoning: the expected loss funds the average cost; VaR sets capital for a chosen confidence; TVaR shows the average cost in the worst 0.5% of years. Reporting only £1.2m as 'the worst case' understates tail risk. The gap between VaR and TVaR also signals severity tail heaviness.
Traps
Calling VaR the maximum loss; ignoring diversification or double counting it; using a model outside its calibrated range; presenting a single number without assumptions; treating regulatory capital as the same as economic capital.