Each scenario is characterised by its exposure to ${() => S.drivers.length}() common risk drivers (e.g. People/Process, Technology, Control Environment). Exposures are scored on a four-point ordinal scale — None (0), Low (1), Medium (2), High (3) — and mapped to continuous values via the vector L = [0, 0.3, 0.6, 1.0]. This produces a scenario-driver matrix B of dimension (N scenarios × K drivers), where B_ik ∈ {0, 0.3, 0.6, 1.0}.

The pairwise correlation between scenarios i and j is computed as a weighted Jaccard overlap of their driver exposure profiles:

where w_k is the weight assigned to driver k (reflecting the relative importance of that root cause in driving correlated losses). The diagonal is set to 1 (a scenario is perfectly correlated with itself). The result is bounded to [0, 0.99] to prevent perfect cross-scenario correlation. This approach ensures that scenarios sharing many high-severity root causes receive high correlation, while unrelated scenarios receive near-zero correlation — without requiring historical loss data.

Within each K-factor bucket, the diversified capital requirement is computed using the standard portfolio variance formula applied to the correlation matrix Σ:

where c_i is the standalone capital estimate for scenario i. This is the same aggregation formula used in market risk VaR models. The diversification benefit is the difference between the simple sum of standalone capitals (Pillar 1 approach) and this portfolio-diversified figure.

Market risk is captured separately for each asset position using parametric VaR:

where σ_daily is the daily price volatility (%), T is the holding period in days, and 2.576 is the 99.5% one-tailed normal quantile. Across positions, a flat correlation ρ (adjustable via slider) is applied: VaR_div = √(Σ VaR_i² + 2ρ Σ_i<j VaR_i·VaR_j).

Counterparty credit risk is modelled using the Basel/Vasicek single systematic factor model, which underpins the IRB approach. The conditional default probability under the worst-case systematic factor realisation at confidence level α is:

where PD is the probability of default, LGD is the loss given default, ρ is the asset correlation with the systematic factor (economy correlation), and Φ is the standard normal CDF. The 99.5% quantile (Φ^-1(0.995) ≈ 2.576) sets the confidence level consistent with the scenario and market VaR approaches. CVaR figures are summed across counterparties (conservative — no inter-counterparty diversification credit is taken).

The OFTR is the sum of: (a) the Pillar 1 floor — max(PMR, KFR_P1, FOR); and (b) the total Pillar 2 add-on — the excess of scenario-diversified capital over the Pillar 1 KFR per K-factor, plus market VaR and counterparty CVaR. No diversification benefit is taken across K-factor buckets, consistent with MIFIDPRU 7.6.3R (no cross-K-factor offsetting). This is a conservative choice that recognises model uncertainty in cross-activity correlations.