Solvency II and insurance regulation

Actuarial function, the best estimate

Valdrenne Insurance SE (invented) is a small EU composite insurer: motor and property insurance, with-profits savings, term assurance and annuities in payment. It reports in € millions at 31 December 2025. The market data team gives the euro swap zero rates, annually compounded, and a one-year average spread between euro IBOR swaps and overnight index swaps of 14bp:

The motor vehicle liability claims already incurred will be paid as below, in € millions, expenses included and with no reinsurance. Take each payment at the end of its year.

Valdrenne does not apply the volatility adjustment today. The risk-corrected spread of the euro reference portfolio is 36bp (illustrative).

Lessons: L4.6.02: Market-consistent valuation and the risk-free curve · L4.6.03: Technical provisions: the best estimate · L4.6.10: Long-term guarantee measures and transitionals

Risk management function, the market module

Valdrenne's investments, at market value in € millions, beside the assets that back its life books:

Only the government bonds and the motor claims of Problem 1 (best estimate €405.55m on the risk-free curve) move with risk-free rates: the floating-rate notes reprice, and the life books are matched by their own assets (illustrative). Today's relative shocks (Arts 166–167) for 1 to 5 years:

EIOPA's equity index stands 14% above its 36-month average. The issuers are diversified and everything is in euro, so concentration and currency risk are nil.

Lessons: L4.6.06: The market risk module

Actuarial function, the underwriting modules

Non-life: two segments, with Annex II's standard deviations. Net earned premiums are for the next and the last 12 months; the claims best estimates are net (the motor one is Problem 1's, rounded).

There is no non-proportional reinsurance, all business is written in one country, and every contract is a one-year policy starting on 1 January, so no further premiums enter the volume. The Annex IV correlation between the two segments is 0.25. The standard formula's non-life cat charge, worked out by the actuarial function, is €48.0m; non-life lapse is nil. Valdrenne's own cat model, if approved as a partial internal model for non-life cat and integrated with the standard formula's correlations, would give €31.0m (illustrative).

Life: the with-profits savings book in three cohorts, in € millions:

The actuarial model gives the other life figures: mortality (rates up 15% on the term book) €24.0m; lapse up (rates up 50%) €12.0m; lapse down (rates down 50%) €6.5m; expense €7.5m. The other life sub-modules are nil. Correlations (Art 136): mortality–lapse 0, mortality–expense 0.25, lapse–expense 0.5.

Lessons: L4.6.07: Counterparty and underwriting modules · L4.6.09: Internal models

Finance and risk, the SCR

The module charges, restated to €0.1m: market 141.1 (Problem 2), counterparty default 18.0 (stated by the risk function, illustrative), life 35.7 and non-life 171.0 (Problem 3, standard formula cat), health nil. Annex IV's correlations between them:

Gross earned premiums over the last 12 months: life 60, non-life 265, with no growth above 20%. Gross best estimates: life 912 (savings 692, term 40, annuities 180; no unit-linked business), non-life 503.6 (motor claims 405.6, property claims 60, premium provisions 25 and 13). There are no discretionary benefits and no intangible assets.

Finance proposes to take the deferred tax adjustment at its ceiling. The tax rate is 25%. The Solvency II balance sheet holds a net deferred tax liability of €12.0m. The recoverability test, on the ORSA plan after a loss the size of the shock, counts pre-tax profits of 40, 40, 40, 20, 10 in years 1 to 5 (the last two after the haircuts the rules ask for) and nothing after.

Lessons: L4.6.05: The standard formula: structure · L4.6.01: The Solvency II architecture

Capital management, own funds

Take the SCR as €234.3m (Problem 4, rounded). Valdrenne's basic own funds, in € millions:

The inputs to the MCR's linear formula: technical provisions net of reinsurance and without the risk margin, net written premiums over the last 12 months, and Annex XIX's factors.

Life (Art 251): with-profits savings, guaranteed benefits 692 at 3.7%; other life obligations (annuities 180, term 40) 220 at 2.1%; total capital at risk on the term book 20,000 at 0.07%. Motor vehicle liability is class 10, so the absolute floor is €4.0m for the non-life business and €4.0m for the life business, added for a composite.

Lessons: L4.6.08: Own funds and the MCR · L4.6.01: The Solvency II architecture

Actuarial function, technical provisions

The actuarial function projects the SCR a reference undertaking would need for Valdrenne's obligations (underwriting, counterparty default on reinsurance and operational risk), in two blocks, in € millions (illustrative):

Discount on the basic risk-free curve of Problem 1, without the VA. The books hold today's risk margin. Hold the SCR at €234.3m and start from the eligible own funds of Problem 5, €452.15m; a change in the risk margin is before tax and falls on Tier 1.

Lessons: L4.6.04: The risk margin · L4.6.12: The 2025 review: Solvency II from 2027 · L4.6.13: Solvency UK and global standards

ALM and risk management

Valdrenne's annuities in payment have a best estimate of €180m on the risk-free curve and a modified duration of 8.5 years. They are backed by an assigned portfolio of corporate bonds held to maturity whose fixed cash flows replicate the payments; assume the conditions for the matching adjustment are met (illustrative). The bonds yield 125bp over the risk-free rate; the part of that spread for expected default and the cost of downgrade is 30bp, and the bonds' long-term average spread is 120bp. The insurer does not use the VA.

Separately, from 30 January 2027 two things change in the interest rate part of the market module: the shocks and one correlation. The 2027 down shock is r(1 − s) − b, floored at −1.25% up to seven years (Delegated Regulation (EU) 2026/269, amending Art 167):

The 2027 up shock still gives a gain on Problem 2's items. Every other sub-module stays as in Problem 2.

Lessons: L4.6.10: Long-term guarantee measures and transitionals · L4.6.12: The 2025 review: Solvency II from 2027 · L4.6.06: The market risk module

Board risk committee and the reporting team

A stress at the end of a quarter: a loss of €230m falls on the reconciliation reserve. The SCR (€234.3m) and the MCR (€105.44m) are unchanged, and so are the notes of Problem 5.

Separately, Valdrenne's Belgian subsidiary, a small non-life insurer, has a financial year that ends on 30 September.

Lessons: L4.6.08: Own funds and the MCR · L4.6.11: Governance, ORSA and reporting