Technical provisions: the best estimate · RiskAtoms Academy

By the end you will be able to

1Decide which cash flows belong in the best estimate: the contract boundary, premiums, benefits and expenses with inflation (Directive Arts 77–78; Delegated Regulation Art 18).
2Value options and guarantees as intrinsic plus time value, and say why the time value needs stochastic scenarios (Art 79; Delegated Regulation Art 32).
3Segment the book into lines of business, split non-life into premium and claims provisions, and show reinsurance recoverables separately with a default adjustment (Arts 80–81).
4Reconcile RiskAtoms Insurance SE's best estimate of €50,921.6m and risk margin to its technical provisions of €52,800m.

Why it matters

Technical provisions are the largest item on an insurer's balance sheet: 85.4% of RiskAtoms Insurance SE's Solvency II liabilities. Small choices inside them, such as which premiums to count, how to value a guaranteed rate, which reinsurer might fail, move own funds by hundreds of millions. Solvency II does not let the insurer pick a prudent number: it asks for the best estimate, and puts the prudence in the risk margin and the SCR.

Core explanation

Probability-weighted, discounted, and gross

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 reads the best estimates Level 3 computed (L3.8.03: Reserve risk, L3.8.08: Lapse and policyholder behaviour) by Solvency II line. It adds one illustrative calculation, the reinsurer default adjustment, which the book itself does not make illustrative.

Art 77 sets the rule in two parts. Technical provisions are the best estimate plus a risk margin (L4.6.04: The risk margin). The best estimate is the probability-weighted average of future cash flows, discounted on the risk-free curve of L4.6.02: Market-consistent valuation and the risk-free curve, on up-to-date and credible information and realistic assumptions, and calculated gross: what the insurer expects back from reinsurers is a separate asset.

Which cash flows: the contract boundary

Every obligation of a contract belongs to it, unless it is cover after a date when the insurer can end the contract, refuse premiums, or reprice it so that premiums fully reflect the risk (Delegated Regulation Art 18(3)). Before that contract boundary, future premiums count, and so does any profit in them. After it, renewals are new business, even when the insurer expects customers to stay.

Inside or outside the boundary?

All the cash flows, expenses included

The cash flows run to the end of the obligations: benefits, premiums inside the boundary, and every expense of servicing the business, with inflation (Directive Art 78). Each book carries its own per-policy expenses, growing at 2% a year:

Book	Expense per policy (€ a year)	Present value (€m)
Annuities in payment	40	112.8
Term assurance	40	159.9
Savings with guarantees	60	387.6
Income protection	30	63.9
All four life and health books		724.2

Options and guarantees

Art 79 and Delegated Regulation Art 32 require the value of every financial guarantee and contractual option, with realistic assumptions on how policyholders use them. The book's savings policies credit the greater of a guaranteed rate and the fund's rate less a 0.75% margin. On the central scenario the guarantee costs its intrinsic value; across 2,000 scenarios with a 2% volatility it costs more, and the difference is the time value:

Cohort	Guarantee	Account value	Intrinsic value	Time value
2005–2012 contracts	3.00%	6,500	600.8	149.5
2013–2017 contracts	1.75%	7,500	85.3	417.0
2018–2025 contracts	0.50%	9,000	0.0	234.6
Savings book		23,000	686.1	801.1

The oldest cohort's 3% guarantee is deep in the money, so most of its cost is intrinsic. The newest cohort's 0.5% guarantee has no intrinsic value at all, yet costs €234.6m: in bad scenarios it bites. A deterministic best estimate of €22,458.4m would understate the savings book by €801.1m.

Segmentation, non-life provisions and recoverables

The best estimate is calculated on homogeneous risk groups, at least by line of business (Art 80). Non-life splits into a premium provision and a claims provision, valued separately (Delegated Regulation Art 36). The book's premium provision, €1,122.4m, is the discounted value of €900m and €250m of claims and expenses on unexpired cover, spread across the lines by premium; the claims provision, €7,091.0m, is L3.8.03: Reserve risk's reserves discounted.

Reinsurance recoverables are an asset, calculated on the same rules and adjusted for the expected loss if the reinsurer defaults (Directive Art 81). Delegated Regulation Art 61 allows a simplified adjustment where proportionate, with PD the reinsurer's one-year default probability:

\text{Adj}_{CD} = -\max\!\Big(0.5 \cdot \frac{PD}{1 - PD} \cdot \text{Dur}_{\text{mod}} \cdot \text{BE}_{\text{rec}};\; 0\Big)

The formal version

An expectation of discounted cash flows

For a homogeneous risk group, with scenarios s of probability p_s, cash flows CF_t^(s) (out minus in) and R(t) the continuous risk-free zero rate:

\text{BE} = \sum_{s} p_s \sum_{t} \text{CF}_t^{(s)}\, e^{-R(t)\,t} \;=\; \mathbb{E}\Big[\sum_t \text{CF}_t\, e^{-R(t)\,t}\Big]

Where cash flows depend on the path, as a guarantee does, the expectation of the payoff is not the payoff of the expectation. For a guaranteed rate g on a fund rate X with mean μ and standard deviation σ (normal, one year):

\mathbb{E}\big[\max(g - X, 0)\big] = (g - \mu)\,\Phi(d) + \sigma\,\varphi(d), \quad d = \frac{g - \mu}{\sigma}, \quad \text{time value} = \text{total} - \max(g - \mu, 0)

Try it

Price one year of each savings cohort's guarantee. The fund rate is the one-year forward, 2.00%, less the 0.75% margin. Move the guarantee towards the fund rate and watch the time value peak; set the volatility to zero and it vanishes.

Try itPrice one year of a guaranteed rate

Start from a cohort of the book

Guaranteed rate g3.00%

Expected fund rate μ1.25%

Volatility σ2.00%

Cost of the guarantee, per €100€1.960

Time value share11%

Intrinsic value, max(g − μ, 0)€1.750

Time value€0.210

On €1,000m of account value€19.6m

Illustrative, one year only and undiscounted. The shaded area is where the fund earns less than the guarantee and the insurer pays the difference. The book values each cohort over its whole term with 2,000 scenarios; this one-year normal floor is a sketch of the same idea.

Worked example

From best estimate to technical provisions

€ millions at 31 December 2025, from the Level 3 book, by Solvency II line of business:

Book	Line of business	Gross BE	Recoverables	Net BE
Annuities in payment	Other life insurance (annuities)	19,928.3	0.0	19,928.3
Term assurance	Other life insurance	−529.5	0.0	−529.5
Savings with guarantees	Insurance with profit participation	23,259.5	0.0	23,259.5
Income protection	Health insurance (similar to life)	49.9	0.0	49.9
Motor liability	Segment 1: Motor vehicle liability insurance and proportional reinsurance	3,154.1	142.7	3,011.4
Motor own damage	Segment 2: Other motor insurance and proportional reinsurance	438.2	0.0	438.2
Property (home and commercial)	Segment 4: Fire and other damage to property insurance and proportional reinsurance	1,589.0	174.7	1,414.2
General liability	Segment 5: General liability insurance and proportional reinsurance	3,032.2	226.6	2,805.5
Total		50,921.6	544.1	50,377.5

Reconcile the best estimate to the balance sheet

Step 1 of 5

1
Life and health
$19{,}928.3 -529.5 + 23{,}259.5 + 49.9 = 42{,}708.2\text{m}$

Savings with guarantees

€23,259m

Annuities in payment

€19,928m

Non-life (4 lines)

€8,213m

Risk margin

€1,878m

Income protection

€50m

Term assurance (negative)

€529m

The reinsurer default adjustment, illustrated

The book holds its non-life recoverables gross of any default adjustment. With the Art 61 simplification, a PD of 0.05% for an A-rated reinsurer and each line's modified duration, the adjustment would be illustrative:

Line	Recoverables	Modified duration	Adjustment
Motor liability	142.7	2.51y	−0.09
Property (home and commercial)	174.7	1.59y	−0.07
General liability	226.6	2.96y	−0.17
Total	544.1		−0.33

Under €0.33m: short-tailed recoveries from strong reinsurers lose little to default. The counterparty default module of the SCR (L4.6.07: Counterparty and underwriting modules) carries the larger, stressed version of the same risk.

Regulatory lens

Directive 2009/138/EC Arts 76–86 and Delegated Regulation (EU) 2015/35 Arts 18, 32, 36 and 61, read in force at 31 December 2025 as at 4 Nov 2026. EIOPA's Guidelines on the valuation of technical provisions (EIOPA-BoS-14/166, revised by EIOPA-BoS-22/217 from 1 January 2023) add detail on boundaries, expenses and simplifications.

In the EU from 2027

from 2027 The amended Directive keeps the best-estimate rules. Its new proportionality measures (Arts 29a–29d) include a prudent deterministic valuation of non-material options and guarantees in life business (Art 77(8)): automatic for small and non-complex undertakings from 30 January 2027, with prior approval for others. RiskAtoms Insurance SE is not small and non-complex (L4.6.01: The Solvency II architecture), and its guarantees are material, so its stochastic valuation stays.

In the UK

UK Since 31 December 2024 the best-estimate rules sit in the PRA Rulebook's Technical Provisions and Technical Provisions – Further Requirements Parts, with supervisory statement SS8/24 on simplifications; the principles here carry over. The UK comparison is in L4.6.13: Solvency UK and global standards.

Art 77(2) probability-weighted, discounted, gross, DR Art 18 contract boundaries, Art 79 options and guarantees, Art 81 recoverables and default.

Spark Atoms

Spark AtomThe guarantee nobody valued

Equitable Life sold pensions with guaranteed annuity rates. When interest rates fell in the 1990s the guarantees became costly; in July 2000 a court ruled that its way of paying for them was unlawful, and the society closed to new business on 8 December 2000. A time value that no one had reserved for came due as intrinsic value.

Spark AtomA liability that is an asset

Term assurance's best estimate is −€529.5m: the expected profit in future premiums inside the boundary. Solvency II counts it in own funds, as expected profits in future premiums, and asks insurers to report how much there is (Delegated Regulation Arts 70(2), 295(5) and 309(6)).

Key takeaways

Technical provisions = best estimate + risk margin. The best estimate is the probability-weighted average of discounted future cash flows, realistic, not prudent, and gross of reinsurance (Art 77).
Only cash flows inside the contract boundary count: future premiums the insurer cannot refuse or reprice are in, renewals it can reprice are not (Delegated Regulation Art 18).
Guarantees cost intrinsic plus time value. On the book: €686.1m + €801.1m = €1,487.2m, and the time value needs scenarios.
Segment by line of business; split non-life into premium and claims provisions; show recoverables as an asset with a default adjustment (Arts 80–81).
RiskAtoms Insurance SE: €50,921.6m + €1,878.4m = €52,800m of technical provisions, €1,200m below IFRS.

Reaction

Check what stuck

Question 1 · objective 1

A motor policy renews on 1 March, when the insurer may reprice it freely. At 31 December, which cash flows of next year's renewal belong in the best estimate?

ANone: cover after the date the insurer can reprice to fully reflect the risk is outside the contract boundaryBAll of them, because most customers renewCThe premiums but not the claimsDThe expected profit only

Question 2 · objective 4

RiskAtoms Insurance SE's gross best estimate is €50,921.6m and its risk margin €1,878.4m. What are its technical provisions, in €m?

€m

Question 3 · objective 2

A one-year guarantee of 3% on a fund expected to earn 1% with a standard deviation of 2% (normal). What is its time value per €100 of account value, in €?

€

Question 4 · objective 2

The book's three savings cohorts carry guarantee costs of €686.1m of intrinsic value and €801.1m of time value. What is the total in the best estimate, in €m?

€m

Question 5 · objective 3

Recoverables of €100m from a reinsurer with a one-year default probability of 0.5% and a modified duration of 4 years. What is the simplified Art 61 default adjustment, in €m (negative)?

€m

Glossary

Best estimate: Best estimate: the probability-weighted average of future cash flows, discounted on the relevant risk-free curve, gross of reinsurance (Directive Art 77(2)).
Contract boundary: Contract boundary: the point after which cash flows no longer belong to an existing contract, because the insurer could end it, refuse premiums or reprice it to fully reflect the risk (Delegated Regulation Art 18(3)).
Intrinsic value: Intrinsic value: what a guarantee costs on the central scenario alone, here max(g − μ, 0) for a guaranteed rate g and an expected fund rate μ.
Time value: Time value: what a guarantee costs on average across scenarios, over and above its intrinsic value. Only a stochastic valuation shows it.
Homogeneous risk group: Homogeneous risk group: a set of policies with similar risks, the unit the best estimate is calculated on. At least the line of business (Art 80).
Premium provision: Premium provision: the best estimate for claims that will happen after the valuation date on cover already written (within the contract boundary), net of premiums still to come.
Claims provision: Claims provision: the best estimate for claims that have already happened, reported or not (Delegated Regulation Art 36).
Reinsurance recoverables: Reinsurance recoverables: the amounts expected from reinsurers, shown as an asset, adjusted for expected losses from the reinsurer's default (Directive Art 81).

Deep Dives & Origins

Deep Dives

L3.8.08: Lapse and policyholder behaviour: how policyholder behaviour and guarantees drive the savings book. Foundation.
L4.6.10: Long-term guarantee measures and transitionals: the long-term guarantee measures that change how these cash flows are discounted. Intermediate.

Origins

Directive 2009/138/EC, Arts 76–81, legislation.gov.uk copy of the EU text.
Commission Delegated Regulation (EU) 2015/35, Arts 18, 32 and 36 as adopted (legislation.gov.uk); Art 61 (EIOPA Solvency II Single Rulebook); Arts 70(2), 295(5) and 309(6) (EUR-Lex text, LawPlayer copy).
Directive (EU) 2025/2, Arts 29a–29d and 77(8) (LawPlayer copy of the OJ text).
EIOPA, Guidelines on valuation of technical provisions, EIOPA-BoS-14/166 (2015), revised by EIOPA-BoS-22/217 (2022).
Prudential Regulation Authority, SS8/24 Solvency II: Calculation of technical provisions, 15 November 2024.
Equitable Life (Payments) Act 2010, Explanatory Notes, paragraph 5 (legislation.gov.uk); D. Baranoff and C. O'Brien, Equitable Life U.K.: a Decade of Regulations and Restructuring, The Geneva Association, 2016.

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