Math Atoms
By the end you will be able to
- 1Date the steps of the 2025 review, from adoption in 2024 to the end of the phase-ins in 2032.
- 2Explain each main change to the numbers: risk margin, interest rate shocks, correlation, symmetric adjustment, long-term equity, extrapolation and the VA.
- 3Apply the changes one at a time and together to a book, and explain why the effects do not add.
- 4Describe the proportionality, macroprudential and reporting changes that move no figure on the book.
Why it matters
Solvency II's first big review took four years from EIOPA's advice to a final text. On RiskAtoms Insurance SE its largest single number, a fall of €605.8m in the risk margin, is partly eaten by an interest rate charge that nearly quadruples. The ratio ends at 190.3%, not the 198.1% the risk margin alone would suggest. Which change wins depends on the book.
Core explanation
What changes on 30 January 2027
Illustrative dataRiskAtoms Insurance SE, under the rules
The same made-up composite insurer as M3.8: Insurance risk, in € millions at 31 December 2025. Its booked figures stand: own funds €9,300m, a Solvency Capital Requirement of €5,000m, a ratio of 186%. L4.6.05: The standard formula: structure rebuilt the standard formula article by article; where Level 3 stated a figure or used its own cat model, the “rules in outline” view computes the formula instead (SCR €5,155.9m, ratio 180.4%). The book applies no long-term guarantee measure, no transitional and no internal model. Every what-if on this page is labelled, holds the deferred-tax adjustment at the book's 19.4% of BSCR plus operational risk, and is before tax. Every policy, bond, treaty and counterparty is invented.
Added here. Each change applied to the year-end 2025 book as if the 2025 review applied that day, with no phase-in. The long-term equity and extrapolation rows are what-ifs. illustrative
TimelineFrom political agreement to full application
1 / 827 Nov 2024
Directive adopted
The changes that move a figure
Risk margin. The cost-of-capital rate falls from 6% to 4.75%, and each future year's SCR is scaled by max(0.96t; 50%) (L4.6.04: The risk margin). The book's risk margin falls from €1,878.4m to €1,272.6m.
Interest rate shocks. Today's shock multiplies rates, so it barely moves rates near zero. From 2027 the stressed rate is r(1 + s) + b, with a floor on the way down (L4.6.06: The market risk module). The book's interest charge goes from €393.0m to €1,529.2m (up binds both times). The Directive lets the Commission phase the new shocks in over up to five years (Art 111(2a)); no phase-in was found in the text of 2026/269 read for this lesson, and none is applied.
Correlation. Spread and interest risk are correlated 25%, not 50%, when the down scenario binds. Symmetric adjustment. Its limits widen from ±10% to ±13%: the book's equity charge can range from €1,141.2m to €2,022.9m, against €1,243.0m to €1,921.2m today. Long-term equity. Simpler conditions for the 22% charge (Art 105a: an average holding period over five years, and the ability to avoid forced sales for five years); if all the book's listed shares qualified, its equity charge would fall from €1,582.1m to €1,076.0m.
Extrapolation and the VA. The curve beyond 20 years follows the 2027 method and the VA becomes 85% × CSSR × RCS; both were worked in L4.6.10: Long-term guarantee measures and transitionals.
| Change, one at a time | Where | Own funds | SCR | Ratio |
|---|---|---|---|---|
| Risk margin: CoC 6% → 4.75%, SCR(t) × max(0.96^t; 50%) | Directive Art 77(5); 2026/269 amending Arts 37(1), 39 | +605.8 | – | 198.1% |
| Interest rate shocks: r(1 + s) + b, down floor −1.25% to −0.893% | 2026/269 amending Arts 166-167 | – | +204.1 | 178.7% |
| Spread–interest correlation in the down scenario 50% → 25% | 2026/269 amending Art 164(3) | – | – | 186.0% |
| Symmetric adjustment limits ±10% → ±13% | Directive Art 106(3); 2026/269 amending Art 172(4) | – | – | 186.0% |
| Long-term equity: simpler criteria for the 22% charge (what-if: all listed shares qualify) | Directive Art 105a; 2026/269 replacing Art 171a | – | −306.1 | 198.1% |
| Extrapolation: FSP 20, α 11% (20% in 2027) instead of Smith–Wilson to 60 | Directive Art 77a; 2026/269 Arts 43a, 46, 46a | +8.1 | – | 186.2% |
| VA redesign: 85% × CSSR × RCS (from 65% × RCS) | Directive Art 77d | – | – | 186.0% |
| Small and non-complex undertakings; scope thresholds €15m GWP / €50m TP | Directive Arts 4, 29a-29e | – | – | 186.0% |
| Combined (first three) | +605.8 | +204.1 | 190.3% |
The changes that move no figure here
Proportionality. The thresholds below which Solvency II does not apply rise to €15m of premiums and €50m of technical provisions (Art 4). New Art 29a defines a small and non-complex undertaking by tests such as non-life premiums up to €100m and life provisions up to €1,000m; RiskAtoms is far above both. Macroprudential tools. The ORSA must look at the macroeconomic situation; firms draw up liquidity risk management plans (Art 144a, with SNCUs exempt); and in exceptional circumstances supervisors may suspend redemption rights (Art 144b) or, in a sector-wide shock, restrict dividends and other distributions (Art 144c). These are macroprudential tools. Sustainability and reporting. Climate scenarios in the ORSA, the split SFCR, longer deadlines (L4.6.11: Governance, ORSA and reporting).
The formal version
A ratio changes when its top or its bottom does. Writing each as a percentage change (M-A01: Percentages) shows why effects do not simply add.
- is today's ratio, 186.0%; the LAC DT as a share of BSCR + Op, held at 19.4%; the module charges and the correlation matrix.
- A change in one module charge moves the BSCR by less than its own size, because of diversification: the interest charge rises by €1,136.2m but the SCR by only €204.1m.
Try it
Switch the changes on in any order and move the equity index. The interest shocks and correlation interact through the square root; the symmetric adjustment's new limits only matter beyond ±10%.
Try itSwitch on 2027, one change at a time
Applied: 0% (limits ±10%). Equity charge €1,582.1m.
As booked at a symmetric adjustment of 0: 186.0%. Before tax; as if the 2027 rules applied at 31 December 2025.
Worked example
RiskAtoms Insurance SE under the 2027 rules
€ millions, 31 December 2025, as if the 2027 rules applied that day, before tax. EU from 2027
One change at a time, then together
Step 1 of 6- 1
Start: today's rules
Regulatory lens
Directive (EU) 2025/2 of 27 November 2024; Delegated Regulation (EU) 2026/269. Status as at 4 November 2026 as at 4 Nov 2026: both adopted and published; the amended rules are not yet applied. National transposition was not checked.
In the EU
In the UK
Spark Atoms
Spark AtomWhy the interest charge nearly quadruples
Spark AtomWhere the EU and the UK landed on the risk margin
Key takeaways
- Directive (EU) 2025/2 and Delegated Regulation (EU) 2026/269 apply from 30 January 2027; the extrapolation and transitionals settle by 1 January 2032.
- Risk margin: CoC 4.75% and a 0.96 taper floored at 50%, worth +€605.8m of own funds on the book.
- Interest shocks r(1 + s) + b: the book's charge rises from €393.0m to €1,529.2m and its SCR by €204.1m.
- Together with the correlation change (no effect here) the ratio goes from 186.0% to 190.3%; ratio effects multiply, they do not add.
- Proportionality (SNCUs, higher thresholds), macroprudential tools and reporting changes move no figure on this book but change how it is run.
Reaction
Check what stuck
Question 1 · objective 1
From what date do the amended Directive and the new Delegated Regulation apply?
Question 2 · objective 3
With the risk margin, interest shocks and correlation changes together, own funds are €9,905.8m and the SCR €5,204.1m. What is the solvency ratio, in %?
Question 3 · objective 2
From 2027 the symmetric adjustment may reach +13%. What is the book's equity charge at that limit, in €m?
Question 4 · objective 2
Why does cutting the spread–interest correlation from 50% to 25% leave the book's SCR unchanged?
Question 5 · objective 2
The risk margin change raises the book's ratio. Which side of the ratio does it move?
Glossary
- The 2025 review
- The 2025 review: Directive (EU) 2025/2 of 27 November 2024 amending the Solvency II Directive, and Delegated Regulation (EU) 2026/269 amending Delegated Regulation 2015/35. Both apply from 30 January 2027.
- 2027 interest rate shock
- Interest rate shock (2027): the stressed rate is r(1 + s) + b at each maturity, with s and b from a table, and a floor on downward moves; replaces today's purely relative shock.
- Symmetric adjustment
- Symmetric adjustment: an addition to the equity shock that rises after equity markets rise and falls after they fall, so the charge is lower after a crash. Limited to ±10% today, ±13% from 2027 (Art 106(3)).
- Long-term equity
- Long-term equity: shares held with the intention and ability to keep them for the long term, which take a 22% equity shock instead of 39% or 49% when the conditions of Art 105a are met.
- SNCU
- Small and non-complex undertaking (SNCU): an insurer that meets the size and risk tests of new Art 29a and so gets proportionality measures without asking, such as a less frequent ORSA and lighter reporting.
- Macroprudential tools
- Macroprudential tools: rules that look at the insurance sector as a whole, such as the ORSA's macroeconomic analysis, liquidity risk management plans and supervisory powers to restrict distributions in an exceptional sector-wide shock.
Deep Dives & Origins
Deep Dives
- L4.6.06: The market risk module: the interest, equity and spread sub-modules before and after. Intermediate.
- L4.6.04: The risk margin: the risk margin and its taper. Intermediate.
Origins
- European Parliament and Council, Directive (EU) 2025/2 of 27 November 2024 amending Directive 2009/138/EC (LawPlayer copy of the Official Journal text).
- European Commission, Delegated Regulation (EU) 2026/269 amending Delegated Regulation (EU) 2015/35 (LawPlayer copy).
- Debevoise & Plimpton, client update on Delegated Regulation (EU) 2026/269, 2026.
- Ashurst, briefing on the Solvency II delegated act adopted 29 October 2025, 2026.
- EIOPA, Consultation paper on liquidity risk management plans and related tools (EIOPA-BoS-24-320), 2024.
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