Solvency II SCR and solvency ratio

Market risk sub-module and BSCR aggregation with the standard formula correlation matrices, operational risk and adjustments, solvency ratio and each module's share.

Inputs

Market risk sub-modules (capital charge after each stress)

Interest rateEquityPropertySpreadCurrencyConcentrationInterest-rate down shock is binding (A = 0.5)

Other modules

Counterparty defaultLifeHealthNon-lifeIntangible assetsOperational riskLoss absorbency of TP and deferred taxEligible own funds

Results

SCR

594

BSCR 626

Solvency ratio

177%

Surplus 456

Market risk

501

685 before diversification

Diversification benefit

220

26.0%

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Modules and their share of the diversified BSCR

Module	Charge	Share of BSCR	%
Market	501	471	75.2%
Counterparty default	35	15	2.3%
Life	180	93	14.9%
Health	40	14	2.2%
Non-life	90	33	5.3%

Methodology

Conventions

Charges are the results of each module's stresses, entered as positive amounts. Market risk is aggregated from its sub-modules with the Article 164 correlations. A is 0 when the interest-rate up shock is the binding one, 0.5 for the down shock.
BSCR aggregates the five modules with the Annex IV correlations and adds the intangible asset charge. SCR = BSCR + operational risk − the loss-absorbing capacity of technical provisions and deferred taxes.
Each module's share of the diversified BSCR uses the Euler allocation, so the shares add up.

References

Directive 2009/138/EC (Solvency II), Annex IV.
Commission Delegated Regulation (EU) 2015/35, Articles 87 and 164.

Formulas

Aggregation: \text{SCR} = \sqrt{\sum_{i,j} \rho_{ij}\,\text{SCR}_i\,\text{SCR}_j}
SCR: \text{SCR} = \text{BSCR} + \text{SCR}_{op} + \text{Adj}
Solvency ratio: \text{Eligible own funds} / \text{SCR}