Counterparty and underwriting modules

Level 3 wrote RiskAtoms' counterparty charge as a round €150m and took its cat charge from its own event model. Both are reasonable guesses, and neither is what the standard formula asks for. The formula wants the reinsurers by name and rating, and the sums insured by region. Supply them and counterparty becomes €267.3m, cat €1,084.3m: 54% more than the insurer's own 1-in-200.

Counterparty default: two kinds of exposure

Art 189 splits exposures in two. Type 1Type 1 exposures: few, usually rated counterparties whose default is diversified only a little: reinsurance, derivatives, cash at bank, letters of credit (Art 189(2)). Charged through a variance across PD classes (Arts 200–201). are few and rated: here six reinsurers holding €3,000m of recoverables and four banks holding €2,000m of cash. Type 2Type 2 exposures: many small, usually unrated ones: receivables from intermediaries and policyholders, mortgage loans and other credit exposures outside the spread sub-module (Art 189(3)). Charged with flat factors, 15% and 90% (Art 202). are many and small: €800m of premiums receivable. Each type 1 counterparty gets a loss given defaultLoss given default (LGD): for reinsurance, 50% of the recoverables plus half the risk-mitigating effect, less collateral (Art 192(2)); for cash at bank, the deposit. and a probability of default from its credit quality step (Art 199): 0.002% for AAA, 0.01% AA, 0.05% A, 0.24% BBB, 1.2% BB, 4.2% below. A reinsurer's LGD includes half of its risk-mitigating effectRisk-mitigating effect (RM_re): how much lower the underwriting (or market) risk charge is because of the reinsurance, the hypothetical charge without it less the actual (Art 196). A reinsurer's default loses that protection as well as the money owed., because a default also takes the cover away (L3.8.10: Reinsurance in depth).

The charge is not a sum of PD × LGD. Art 201 builds a variance from two parts: V_inter, which treats counterparties in different PD classes as correlated through the economy, and V_intra, which adds the lumpiness of a few large names within a class. Here V_inter is 1,692.0 and V_intra 354.7, so σ = €45.2m, 1.17% of total LGD. Below 7% the charge is 3σ (Art 200): €135.7m. Type 2 is €150m, and the two combine as √(T1² + 1.5·T1·T2 + T2²) = €267.3m rules.

The variance weighs both size and quality. Put all €3,000m with one A-rated reinsurer and type 1 becomes €198.0m, the module €325.9m; with one AA reinsurer it is €132.5m, because the better rating offsets the concentration. All the cash at one bank gives €162.8m; the six reinsurers one step lower each, €190.2m. Reinsurance always trades underwriting risk for counterparty risk (L2.6.07: Insurance and reinsurance); the standard formula prices the trade.

Non-life: premium and reserve

Premium risk is that next year's claims on next year's premiums are worse than expected; reserve risk that the claims already incurred cost more than reserved (L3.8.04: Premium risk and the underwriting cycle). Art 115 charges both together as 3 × σ_nl × V_nl, where each segment's volumeVolume measures: V_prem is the larger of next year's and last year's net earned premium, plus expected premiums on existing and future contracts (Art 116(3)); V_res is the net best estimate of claims outstanding. is premium plus reserve, and its standard deviationStandard deviation σ: Annex II sets σ_prem and σ_res for each of 12 segments. They are combined within a segment, then across segments with Annex IV's correlations, into σ_nl. blends Annex II's σ_prem and σ_res with a correlation of 0.5. σ_prem is multiplied by 80% for non-proportional reinsurance in segments 1, 4 and 5: motor vehicle liability, fire and other damage to property, and general liability (Art 117(3)).

Combined across segments with Annex IV's correlations, σ_nl × V_nl = 847.1 against 1,154.4 added up; the charge is 3 × 5.74% × 14,746.9 = €2,541.3m. Level 3 simplifies in two directions: it leaves out the expected premiums of existing and future contracts in V_prem (Art 116(3)), which would raise the volume, and the geographical diversification of Annex III, which would lower it. A firm may replace some σ with undertaking-specific parameters from its own data, with supervisory approval (Directive Art 104(7)).

Non-life: lapse and catastrophe

Non-life lapse (Art 118) is the loss if 40% of policies ended where that raises technical provisions; it bites only when the premium provision counts future profits, which RiskAtoms' does not, so it is nil. Catastrophe (Art 119) combines four parts: natural catastrophe with non-proportional property reinsurance, man-made (motor, marine, aviation, fire, liability, credit), and other, as √((nat + NP)² + man-made² + other²). The nat catNatural catastrophe sub-module: windstorm, earthquake, flood, hail and subsidence, as specified losses Q × weighted sums insured in each region, run through two-event scenarios net of reinsurance (Arts 120–125). sub-module, in outline on RiskAtoms' zones illustrative:

Fire, on the largest concentration of buildings within a 200-metre radius (here one building, €160m gross; Art 132), costs €2m net of the surplus treaty and per-risk cover. So cat is €1,084.3m against the event model's €703.2m, and the non-life module, premium and reserve and cat combined at 0.25, becomes €3,002.0m against €2,801.2m. The standard formula's scenarios are calibrated to a market-average portfolio, not to RiskAtoms' zones; a firm whose own model says less can ask to use a partial internal model (L4.6.09: Internal models). Catastrophe modelling: L3.8.05: Catastrophe risk.

Life: seven shocks

Each life sub-module is an instant, permanent change to one assumption, and the charge is the fall in own funds it causes, applied only to the policies where it hurts:

Longevity dominates: the annuity book loses €1,887.2m if mortality falls 20% (L3.8.07: Longevity risk), while the term book loses €206.5m if it rises 15% (L3.8.06: Mortality risk). The two are correlated −0.25 in the matrix: a firm with both is partly hedged. Lapse is the largest of up 50%, down 50% (at most 20 points) and mass lapseMass lapse: the instant discontinuance of 40% of policies (70% for some group pension business) where that would raise technical provisions (Art 142(6)).: here mass, at €431.2m (L3.8.08: Lapse and policyholder behaviour). The seven add to €2,722.8m; the matrix gives €2,054.0m.

Health

Health splits by technique: similar-to-life (SLT) health mirrors the life sub-modules, not-similar-to-life (NSLT) health mirrors non-life premium, reserve and lapse, and health catastrophe adds mass accident, accident concentration and pandemic (Arts 144–163). SLT and NSLT correlate 0.5; catastrophe 0.25 with both. RiskAtoms' income protection is SLT: disability-morbidity €191.3m (35% more incidence in year one, 25% after, and 20% less recovery where recovery rates are below 50%; Art 156) and expense €13.0m, combined at 0.5 to €198.1m (L3.8.09: Expense, health and morbidity risk). Level 3 leaves out SLT lapse and revision and health cat.

Delegated Regulation (EU) 2015/35 Arts 114–117, 119, 136–143, 189–202:

• $TLGD_j$ is the total LGD of counterparties with PD $p_j$. The 1.25 and 1.5 are calibration constants; the variance is a sum over pairs, like $s^{\top}Cs$ (M-C06: The normal distribution).
• Every shock is a percentage of a rate, a volume or a sum insured (M-A01: Percentages); applied per policy, only where it raises technical provisions.

Concentrate the panel, downgrade it, take away the risk-mitigating effect, and let receivables go overdue. Watch σ move against ΣLGD: if σ passes 7% of ΣLGD the charge jumps from 3σ to 5σ. A four-step downgrade gets there whether one reinsurer holds all the reinsurance or the panel of six shares it, the panel only just (7.05% against 9.84%).

RiskAtoms' sums insured by country from Level 3's zones, every risk weight 1, regions run through the cat XL (€500m xs €500m and €1,000m xs €1,000m, one reinstatement each) illustrative.

With counterparty at €267.3m as well, the SCR on the rules in outline is €5,155.9m and the ratio 180.4% (L4.6.05: The standard formula: structure).

Delegated Regulation (EU) 2015/35 Arts 114–163 (underwriting) and 189–202 (counterparty), with Annexes II and V–VIII; Directive 2009/138/EC Arts 104–105 as at 4 Nov 2026.

Results are disclosed by module in the SFCR, with the detail of each sub-module in the quantitative reporting templates sent to the supervisor (L4.6.11: Governance, ORSA and reporting).

• Counterparty default: type 1 (reinsurers, banks, derivatives) from a variance over PD classes, 3σ, 5σ or ΣLGD; type 2 at 15% and 90%; combined with 1.5·T1·T2. RiskAtoms: €135.7m + €150m → €267.3m.
• Reinsurer LGD = 50% × (recoverables + 50% × RM_re): a default loses money owed and protection. Concentration and downgrades raise the charge.
• Non-life premium and reserve = 3σ_nl V_nl from Annex II's σ by segment (€2,541.3m); lapse nil here; cat = √((nat + NP)² + man-made² + other²).
• Nat cat in outline: Q × sums insured by region, two-event scenarios net of reinsurance, regions and perils aggregated: €1,084.3m, against €703.2m from Level 3's own model.
• Life: mortality +15%, longevity −20%, disability, lapse ±50% or mass 40%, expense +10% and +1 point, revision 3%, cat +0.15 points; 7×7 matrix. Health: SLT, NSLT and cat, with 0.5 and 0.25.

Type 1 exposures

Type 1 exposures: few, usually rated counterparties whose default is diversified only a little: reinsurance, derivatives, cash at bank, letters of credit (Art 189(2)). Charged through a variance across PD classes (Arts 200–201).

Type 2 exposures

Type 2 exposures: many small, usually unrated ones: receivables from intermediaries and policyholders, mortgage loans and other credit exposures outside the spread sub-module (Art 189(3)). Charged with flat factors, 15% and 90% (Art 202).

Loss given default (LGD)

Loss given default (LGD): for reinsurance, 50% of the recoverables plus half the risk-mitigating effect, less collateral (Art 192(2)); for cash at bank, the deposit.

Risk-mitigating effect (RM_re)

Risk-mitigating effect (RM_re): how much lower the underwriting (or market) risk charge is because of the reinsurance, the hypothetical charge without it less the actual (Art 196). A reinsurer's default loses that protection as well as the money owed.

Volume measure

Volume measures: V_prem is the larger of next year's and last year's net earned premium, plus expected premiums on existing and future contracts (Art 116(3)); V_res is the net best estimate of claims outstanding.

Standard deviation by segment

Standard deviation σ: Annex II sets σ_prem and σ_res for each of 12 segments. They are combined within a segment, then across segments with Annex IV's correlations, into σ_nl.

Natural catastrophe sub-module

Natural catastrophe sub-module: windstorm, earthquake, flood, hail and subsidence, as specified losses Q × weighted sums insured in each region, run through two-event scenarios net of reinsurance (Arts 120–125).

Mass lapse

Mass lapse: the instant discontinuance of 40% of policies (70% for some group pension business) where that would raise technical provisions (Art 142(6)).