The Euro_FR_S Model

Reference liability cash flow model for the French euro support (fonds en euros).

Euro_FR_S is the executable counterpart of products/assurance_vie_euro/technical-notes.md in the lifelib-products library. It projects gross best-estimate liability cash flows for single model points on the euro support of a contrat d’assurance vie — the standardized composite specified in product-spec.md, not any single insurer’s fund — together with the two state variables that make the product what it is: the épargne acquise and the provision pour participation aux bénéfices (PPB).

The rate is an allocation, not an assumption. That sentence is the model. Every year the insurer builds the compte de participation aux résultats that art. A132-11 of the Code des assurances prescribes — 85% of the compte financier, plus the compte technique less the greater of 10% of it and 4.5% of premiums — and the whole of that balance must reach policyholders. What the insurer chooses is only when: what it does not credit this year is carried to the PPB, and what it carried in an earlier year it may credit now. The credited rate taux servi is therefore the statutory floor moved up or down by the PPB lever, floored again by the taux minimum garanti, and never by an assumption typed into a table.

The eight-year clock is a deadline, not an average. A dotation carried to the PPB in financial year v must be applied to mathematical provisions or paid to policyholders within the eight financial years that follow. The model therefore carries a per-vintage ledger, ppb_vintage_pp(y, v) on the financial-year clock, released oldest-first, so that the clock is a real date on a real balance. Modelling the PPB as a single pot with an average age would meet the eight-year rule on average and breach it on every vintage.

The `effet cliquet` is asserted, not assumed. Credited participation aux bénéfices is definitively acquired and cannot be called back, so check_cliquet() asserts that the credited interest is never negative and that the cumulative-PB ledger never falls. What the ratchet does not say is that the account never falls: under the garantie nette the frais de gestion sur encours keeps biting in a nil-PB year, and both statements are true at once.

Spaces. The model contains two:

Data

Reads the four input CSVs and holds their filename References. It takes no parameters, so each file is read once per model.

Projection

The by-policy projection, parameterized by point_id: Projection[1] is an ItemSpace projecting model point 1, the notes’ worked example. It reaches the input tables through its data Reference, which resolves to the single Data Space.

The split matters for more than tidiness. Because Projection is parameterized, every Projection[N] is a separate ItemSpace with its own cells cache; readers placed there would re-read every file for every policy. In Data they are evaluated once, however many policies are projected.

Input data is external: CSVs in the model folder’s parent directory, read at run time rather than stored inside the model. The model folder itself holds no data, so the model and its inputs must travel together.

Projection basis. Monthly steps, because the movements the contract actually bills monthly — the versements libres programmés, the rachats partiels programmés — and the decrements that end a contract are continuous, while the crediting machinery is not. t counts policy months from the valuation date and is 0-based: t = 0 is the first projected month, month t runs from time t / 12 to (t + 1) / 12, and the frame is t = 0 … proj_len() − 1 with proj_len() = 12 * proj_years = 480 months. The contractual policy year is the 1-based label derived from it, policy_year(t) = duration_init + t // 12 + 1, and the attained age — age last birthday — is issue_age + duration_init + t // 12, so both step at the policy anniversary and never inside the year. Versements and rachats partiels fall at the beginning of the month, the insurer’s expense accrues through it, and deaths and rachats totaux act at its end, deaths first.

Underneath that grid the product carries an annual layer, indexed by the projection year y = t // 12, and it is left whole. The participation aux bénéfices is fixed for the closing financial year and credited at 31 December value date, the art. A132-16 PPB clock counts financial years, and the frais de gestion and the prélèvements sociaux land with the interest they are struck on — so the whole of the year’s revalorisation, charge and levy arrives in the anniversary month, is_anniv(t), and eleven months of twelve carry none of it. The crediting base pm_avg_pp(y) is built from the twelve monthly movements at the mid-month weight (11.5 − k)/12, the twelve weighted twelfths of which sum to exactly one half — so the notes’ AV + 0.5 P − 0.5 W is derived here rather than asserted. Decrements follow the library’s two-speed convention: mort_rate(t) and lapse_rate(t) are the annual rates of the policy year containing month t, and mort_rate_mth(t) and lapse_rate_mth(t) are the monthly rates actually applied, 1 − (1 − r)^(1/12).

Because those monthly rates compound back to the annual ones and every contractual event sits on a year boundary, the in force and every financial-year quantity at every anniversary are exactly what the annual-step model this replaced carried. The cash flows are not, and are not meant to be: instalments are collected from a block that decrements every month, expenses accrue where they are incurred, and a claim falls at the end of the month of exit — which also means a mid-year dénouement is now paid the account value without the year’s taux servi, the contractual floor rate pro rata temporis at the nil TMG every model point carries, rather than the full year’s credit an annual grid was forced to give it. result_cf_annual() sums the frame into projection years so the two can be read side by side.

`Prélèvements sociaux` are inside the account and outside ``net_cf``. The 17.2% levy is withheld as the interest is credited, every year, because the rights are expressed in euros — this is the euro fund’s signature mechanic and the commonest foreign-model error. It sits inside the account roll-forward, because it is money that genuinely leaves the contract; it sits outside net_cf, because it is a policyholder tax the insurer remits to the State rather than a benefit or an insurer expense. It has its own soc_levy column so a fund-level asset projection can add it back in one step.

What is sourced and what is not. The mechanics are sourced: the A132-11 split and which limb attaches to which account, the A132-12 minimum benefit, the eight-year PPB release horizon, the effet cliquet, the garantie nette capital floor and its measurement before levies, the death benefit being the account value and nothing more, the absence of a surrender charge, and the annual timing of the social levies. Every rate is a standardization: no insurer publishes its dotation or release policy, no French euro-fund lapse experience is public, no contract in the source set publishes a TMG, and the statutory mortality tables are cited but not redistributable — the shipped table is an INSEE-shaped proxy. This model is a mechanics demonstration, not a pricing or reserving result.

Verification. tests/test_assurance_vie_euro_fr.py asserts the notes’ worked example row by row to the cent — the taux servi and PPB table, the épargne acquise roll-forward, the year-5 trace at full precision, the twelve-year levy and account identities, and the PPB clock closing exactly at its last date — and then one test per modelling pitfall the notes list, plus the monthly grid’s own invariants: that twelve monthly decrements compound back to the annual ones, that the revalorisation and the levy land only in the anniversary month, and that result_cf_annual() is the monthly frame regrouped rather than a second projection.

Example

>>> import modelx as mx
>>> model = mx.read_model("products/assurance_vie_euro/Euro_FR_S")
>>> model.Projection[1].result_cf()