Know these first
- L1.8.04: An insurer’s balance sheet
- L2.7.05: Solvency I to Solvency II
- L3.8.01: How insurers take risk
- L3.8.12: Insurer investment risk and the ORSA
Math Atoms
By the end you will be able to
- 1Place each Solvency II text in its layer (Directive, Delegated Regulation, technical standards, EIOPA Guidelines) and say whom it binds and how.
- 2Decide whether a firm is in scope, today and from 30 January 2027, and explain proportionality and the new small and non-complex undertakings.
- 3State the SCR's calibration in Article 101(3) and read a 99.5% one-year VaR of basic own funds as a quantile.
- 4Read RiskAtoms Insurance SE's Solvency II balance sheet and ratio as booked: own funds €9,300m, SCR €5,000m, 186.0%.
Why it matters
RiskAtoms Insurance SE reports one number to its board each quarter: 186.0%. Behind it sit about 300 articles of a directive, a longer delegated regulation, technical standards for every template, and EIOPA guidelines on how to read them all. Level 3 built that number in outline. This module reads the rules behind it, article by article, and starts here: which text says what, who it applies to, and what the SCR is meant to measure.
Core explanation
Who writes the rules, who they bind, and what they measure
Illustrative dataRiskAtoms Insurance SE under Solvency II
The same made-up composite insurer as Modules 1.8, 2.2 and 3.8, reporting in € millions at 31 December 2025: €70bn of IFRS assets, €9.0bn of non-life premiums, annuities, savings with guarantees, term assurance and income protection. Level 3 booked own funds of €9,300m against an SCR of €5,000m, a ratio of 186%; those stay the insurer's figures. Module 4.6 reads them against the rules article by article: Directive 2009/138/EC and Delegated Regulation (EU) 2015/35 as in force at that date, and the 2025 review where it applies from 30 January 2027. Every policy, bond and figure is invented. Where a page adds an assumption of its own, it is labelled illustrative.
This page uses the insurer's balance sheet and SCR as Level 3 booked them, and adds nothing to them.
L2.7.05: Solvency I to Solvency II introduced the three pillars: quantitative requirements, governance and supervision, reporting and disclosure. In the Directive they map onto chapters you will meet across this module:
| Pillar | Directive 2009/138/EC | Where in this module |
|---|---|---|
| 1 Quantitative | Valuation Art 75; technical provisions Arts 76–86; own funds 87–99; SCR 100–127; MCR 128–131; investments 132–135 | L4.6.02 to L4.6.10 |
| 2 Governance and review | Governance Arts 41–50, including the ORSA (Art 45); supervisory review (Art 36); capital add-ons (Art 37) | L4.6.11; Module 4.9 |
| 3 Reporting and disclosure | Information to supervisors (Art 35); the solvency and financial condition report (Arts 51–56) | L4.6.11 |
Four layers of text
Solvency II follows the pattern the Lamfalussy report proposed for EU securities law in 2001: short principles agreed by the legislators, detail written by the Commission, convergence work by the supervisors, and enforcement. Click each layer.
ExploreFrom principle to practice
Click a layer to see who writes it and how it binds.
Level 1: Directive
Directive 2009/138/EC, applying since 1 January 2016 (Art 311, as replaced by Omnibus II, Directive 2014/51/EU). Amended by Directive (EU) 2025/2 of 27 November 2024, which member states transpose by 29 January 2027 and apply from 30 January 2027 (its Art 4). Example: the SCR's calibration in Art 101(3).
Sort itWhich layer sets it?
Place each rule in the text that sets it.
The SCR is a 99.5% one-year value at risk of basic own funds.
The credit risk adjustment to swap rates is between 10bp and 35bp.
From 2027 firms with at most €15m of premiums and €50m of provisions are outside the regime.
The layout of the quarterly balance sheet template sent to the supervisor.
A ranked list of ways to simplify the projection of future SCRs for the risk margin.
Goodwill is valued at zero.
Who is in scope
Art 4 keeps very small insurers out, if they meet every condition: premiums and technical provisions at or below the thresholds, the same provisions test for their group, no liability, credit or suretyship business beyond ancillary risks, and only a little reinsurance accepted. The 2025 review raises the thresholds:
| Art 4(1) | Until 29 Jan 2027 | From 30 Jan 2027 | RiskAtoms Insurance SE |
|---|---|---|---|
| Annual gross written premiums | €5m | €15m | €11,287m |
| Technical provisions, gross of recoverables | €25m | €50m | €52,800m |
Inside the regime, the rules apply with proportionality (Art 29(3)). From 30 January 2027 the Directive makes that concrete. A firm that meets the tests of Art 29a for two years running notifies its supervisor, which has two months to object (Art 29b); it is then a small and non-complex undertaking and may use the listed proportionality measures without asking (Art 29c), such as an ORSA every two years instead of every year (Art 45(5)) or a prudent deterministic value for immaterial life options and guarantees (Art 77(8)). Any other firm needs the supervisor's prior approval for each measure (Art 29d).
RiskAtoms Insurance SE is a mixed undertaking under Art 29a(1)(c): life and health provisions are 84% of its best estimates and non-life premiums 80% of its €11,287m of premiums. Five of the nine tests can be run on the book:
| Art 29a(1)(c) test | Book | Limit | Result |
|---|---|---|---|
| Life technical provisions at most €1,000m | €42,708m | €1,000m | fails |
| Non-life gross written premiums at most €100m | €9,000m | €100m | fails |
| Interest rate risk charge at most 5% of technical provisions | 0.74% | 5% | meets |
| Net combined ratio below 100% (three-year average; 2025 shown) | 95.0% | 100% | meets |
| SCR covered | 186.0% | 100% | meets |
The interest rate charge of €393.0m (L3.8.11: Insurer asset-liability management) is well inside its test, but life provisions of €42,708m and non-life premiums of €9,000m are far beyond theirs. This insurer applies the full regime, and proportionality for it means only Art 29(3) and any measure its supervisor approves.
What the SCR measures
Art 101(3) fixes the calibration in four sentences:
The Solvency Capital Requirement shall be calibrated so as to ensure that all quantifiable risks to which an insurance or reinsurance undertaking is exposed are taken into account. It shall cover existing business, as well as the new business expected to be written over the following 12 months. With respect to existing business, it shall cover only unexpected losses. It shall correspond to the Value-at-Risk of the basic own funds of an insurance or reinsurance undertaking subject to a confidence level of 99.5% over a one-year period.
Three choices are packed in. The measure is value at risk, a quantile (M-C09: Quantiles), not the average loss beyond it. The confidence level is 99.5%, a one-in-200-year loss. And the quantity at risk is basic own funds, the whole market-consistent balance sheet, so a fall in asset values and a rise in technical provisions count alike. Expected losses are already in the best estimate; the SCR is for the surprise. Art 101(4) lists the risks it must cover at least: non-life, life and health underwriting, market, credit and operational risk.
The formal version
Let be the loss in basic own funds over the next year, in today's money (Directive Arts 88 and 101(3)):
- and are assets and liabilities valued under Art 75 and the technical provision rules (L4.6.02: Market-consistent valuation and the risk-free curve to L4.6.04: The risk margin).
- The VaR is the 99.5% quantile of . For a normal loss with mean zero and standard deviation , it is .
- The standard formula (L4.6.05: The standard formula: structure) does not compute a quantile directly: it applies shocks each calibrated to that standard, and combines them with correlations. An internal model (L4.6.09: Internal models) estimates the distribution itself.
Try it
Suppose, for illustration, the insurer's one-year loss were normal with the standard deviation that makes its 99.5% VaR exactly €5,000m: €1,941m. Move the confidence level, switch to expected shortfall, then fatten the tails and watch the capital.
Try itThe SCR as a quantile of the one-year loss
Risk measure
Shape of the loss
Illustrative, € millions. The loss has mean zero and a standard deviation of €1,941m, chosen so that the normal 99.5% VaR is the book's SCR. The t has the same standard deviation, so only the tail changes. The book's SCR comes from the standard formula, not from a fitted distribution.
Worked example
RiskAtoms Insurance SE's balance sheet and ratio, as booked
€ millions at 31 December 2025. Every figure is in Module 1.8 or the Level 3 book; this lesson only lays them out the way Solvency II reads them.
From the IFRS balance sheet to the ratio
Step 1 of 5- 1
Assets at Solvency II values
Goodwill is valued at zero, and other intangibles too unless they could be sold separately and quoted prices in active markets show a value for the same or similar assets (Delegated Regulation Art 12). Investments are already at fair value.
| Module 1.8's bridge | €m |
|---|---|
| IFRS equity | 7,000 |
| Goodwill and intangibles at zero | −500 |
| Technical provisions revalued (54,000 → 52,800) | 1,200 |
| Subordinated debt counted as Tier 2 | 2,000 |
| Foreseeable dividends | −400 |
| Solvency II own funds | 9,300 |
Regulatory lens
The base is Directive 2009/138/EC and Delegated Regulation (EU) 2015/35 as in force at 31 December 2025. The 2025 review (Directive (EU) 2025/2 and Delegated Regulation (EU) 2026/269) applies from 30 January 2027; L4.6.12: The 2025 review: Solvency II from 2027 works it through. Statements on where rules stand are as at 4 November 2026 as at 4 Nov 2026.
In the UK
Groups, the US approach and the IAIS Insurance Capital Standard are in L4.6.13: Solvency UK and global standards; the supervisory review of the ORSA in M4.9: Supervision, stress testing and disclosure.
Spark Atoms
Spark AtomNext door, 99% expected shortfall
Spark AtomFour levels, borrowed from securities law
Key takeaways
- Directive 2009/138/EC sets principles; Delegated Regulation 2015/35 the detail and every factor; RTS and ITS the formats; EIOPA Guidelines bind by comply or explain.
- Art 4 keeps out firms below €5m of premiums and €25m of provisions, and from 30 January 2027 below €15m and €50m, if they meet every condition.
- From 2027, small and non-complex undertakings (Art 29a) may use the listed proportionality measures after notifying; other firms need approval for each.
- The SCR is the 99.5% one-year VaR of basic own funds, covering unexpected losses on existing business and the next 12 months' new business (Art 101(3)).
- RiskAtoms Insurance SE: assets €69,500m, technical provisions €52,800m, own funds €9,300m against an SCR of €5,000m: 186.0%; MCR ratio 344.4%.
Reaction
Check what stuck
Question 1 · objective 1
Where is the 6% cost-of-capital rate for the risk margin set today?
Question 2 · objective 4
RiskAtoms Insurance SE has eligible own funds of €9,300m and an SCR of €5,000m. What is its solvency ratio, in %?
Question 3 · objective 4
How much own funds does the insurer hold above its SCR, in €m?
Question 4 · objective 2
A local mutual writes €12m of motor premiums a year and holds €30m of technical provisions. Is it inside Solvency II on 1 March 2027?
Question 5 · objective 3
If a firm's one-year loss in basic own funds were normal with mean zero and a standard deviation of €1,000m, what would the 99.5% VaR be, in €m?
Glossary
- Directive 2009/138/EC
- Directive 2009/138/EC (Solvency II): the Level 1 text, agreed by the European Parliament and the Council. Member states transpose it into national law. It sets the principles, such as the SCR's calibration (Art 101).
- Delegated Regulation (EU) 2015/35
- Delegated Regulation (EU) 2015/35: the Commission's Level 2 text that fills in the Directive's detail, such as every standard formula factor. As a regulation it applies directly, with no transposition.
- Technical standards (RTS, ITS)
- Technical standards: rules EIOPA drafts and the Commission adopts as regulations, either regulatory (RTS) or implementing (ITS), under Regulation (EU) No 1094/2010, Arts 10 and 15. The reporting templates are an ITS.
- EIOPA Guidelines
- EIOPA Guidelines: Level 3 texts. Supervisors and firms must make every effort to comply, and each supervisor says within two months whether it complies or why not: comply or explain (Regulation 1094/2010, Art 16(3)).
- Proportionality
- Proportionality: applying the rules in a way that fits the nature, scale and complexity of a firm's risks (Directive Art 29(3)).
- Small and non-complex undertaking
- Small and non-complex undertaking (SNCU): from 30 January 2027, a firm that has met the tests of Art 29a for two years running and notified its supervisor. It may then use the Directive's proportionality measures without asking first.
- Basic own funds
- Basic own funds: the excess of assets over liabilities on the Solvency II balance sheet, plus subordinated liabilities, less own shares held (Directive Art 88).
- Value at risk (99.5%)
- Value at risk (VaR) at 99.5%: the loss that is exceeded with probability 0.5%, the 99.5% quantile of the loss distribution: a one-in-200-year loss over one year.
- Reconciliation reserve
- Reconciliation reserve: the Tier 1 item that collects the rest of the excess of assets over liabilities after share capital and other listed items, less foreseeable dividends.
Deep Dives & Origins
Deep Dives
- L4.6.05: The standard formula: structure: how the standard formula builds the SCR from its modules. Intermediate.
- L4.6.12: The 2025 review: Solvency II from 2027: every change of the 2025 review, worked on this insurer. Intermediate.
Origins
- Directive 2009/138/EC (Solvency II), Arts 4, 29, 75, 88, 101, 129(3) and 311, legislation.gov.uk copy of the EU text.
- Directive (EU) 2025/2 of 27 November 2024 amending Directive 2009/138/EC, Arts 1 (new Arts 4(1), 29a–29d) and 4 (transposition and application), LawPlayer copy of the Official Journal text.
- Commission Delegated Regulation (EU) 2015/35, Arts 12, 15, 39, 45, 58 and 82(2) as adopted; Commission Delegated Regulation (EU) 2026/269 of 29 October 2025, OJ L of 18 February 2026, Art 2.
- Regulation (EU) No 1094/2010 establishing EIOPA, Arts 10, 15 and 16; Commission Implementing Regulation (EU) 2023/894 of 4 April 2023 (reporting templates).
- EIOPA, Guidelines on the valuation of technical provisions, EIOPA-BoS-14/166, and Final report on the revision of the Guidelines, EIOPA-BoS-22/217, 21 April 2022.
- Committee of Wise Men (chair A. Lamfalussy), Final Report on the Regulation of European Securities Markets, Brussels, 15 February 2001.
- Prudential Regulation Authority, PS2/24 Review of Solvency II: Adapting to the UK insurance market, 28 February 2024; Swiss Re, Financial Condition Report 2018, methodology and valuation (SST risk measure).
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