The UC_FR_S Model

Reference liability cash flow model for a French multisupport contract, UC leg.

UC_FR_S is the executable counterpart of products/assurance_vie_uc/technical-notes.md in the lifelib-products library. It projects gross liability cash flows for a single-policy model point of a standardized contrat d’assurance vie multisupport: a single premium split between one composite unités de compte support and one fonds en euros, a management charge levied monthly by cancelling units, and an optional age-rated garantie plancher — a floor death benefit charged on the capital sous risque.

The decomposition is the model. French practice splits this contract exactly as UK practice splits a unit-linked bond, and so does this implementation:

the unit leg — a count of units valued at an exogenous liquidation value. Art. A. 132-5 requires every contract to state that the insurer commits on the number of units and not on their value, so the count is the state variable, every charge is a unit cancellation, and — while the plancher premium is taken from the euro support — the count is a deterministic, market-independent sequence; and

the non-unit cash flow — what accrues to the insurer: the premium charge, the UC management charge, the arbitrage fee and the plancher premium, less expenses and the plancher death strain, which is exactly the capital sous risque and nothing else, because the whole of the account value is funded by cancelling units and by the euro balance.

The garantie plancher is the insurance content. Its charge base is the net amount at risk, not the account value: on the anchor cell at t = 11 the correct charge is 27.18 € and the charge on the account value would be 126.35 €, a factor of 4.6. The net amount at risk is floored at zero, so the rider costs nothing while the units are above the floor and the strain never turns into a rebate; it is capped at 300,000 €, and the cap applies to the risk rather than to the benefit. check_nar_bounds() and check_unit_roll_fwd() assert both.

The euro leg is a pointer. It enters as an allocation share carrying an annual credited rate net of its own management charge, because that is all the UC leg needs it for — the euro balance sizes the capital sous risque and is the first source the plancher premium is levied from. Taux minimum garanti, participation aux bénéfices, the provision pour participation aux bénéfices and the effet cliquet belong to products/assurance_vie_euro/ and model Euro_FR_S, and are neither restated nor re-implemented here. Reading net_cf as the contract’s total margin is therefore a modeling error: it is the UC leg plus the rider, and the euro leg’s margin must be added from outside.

Spaces. The model contains two:

Data

Reads the five 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. 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, t counting policy months from issue and 0-based: t = 0 is the issue month, period t runs from time t to time t + 1, and the frame is t = 0 … proj_len() − 1, so result_cf() has proj_len() rows. A contractual policy year is the 1-based label t // 12 + 1. Within month t: the liquidation value moves and the euro leg accrues; the management charge is taken on the units held at the start of the month; arbitrages and withdrawals settle; the capital sous risque is observed; the plancher premium is levied; decrements act at the end of the month, deaths before surrenders. The balances at issue are not a row of the frame — they are the *_init cells, read into month 0 through the opening cells units_open, unit_price_open, av_euro_open_pp and av_pp_at(t, "OPENING"). Age is age last birthday and the tariff steps at each policy anniversary. The projection runs for the model point’s own proj_len months — the contract is whole of life and has no maturity date.

What is sourced and what is not. The contractual mechanics are sourced: the unit count as the thing guaranteed, the death benefit as the account value plus the capital sous risque, the 300,000 € cap with the excess reducing the floor, cessation at attained age 75, the charge on the net amount at risk by attained age, the levy from the euro support first, the pro-rata split of a partial surrender, the surrender value as the account value with no exit charge, the prélèvements sociaux at 17.2% levied on the UC leg only at dénouement, and the Spirica tariff itself. Every rate is a standardization. No insurer publishes the mortality table, the age definition, the loading or the margin behind a plancher tariff, no French persistency or arbitrage study was retrieved, and no unit-return assumption is published, so the mortality basis, the surrender table, the charge levels and the return scenarios are placeholders. This model is a mechanics demonstration, not a pricing or reserving result.

Verification. tests/test_assurance_vie_uc_fr.py asserts the notes’ worked example to the centime — the month-by-month unit count, account values, floor and net amount at risk, the four plancher_basis variants on the same path, the settlement arithmetic of the partial surrender, and the insurer-side extraction beside it — plus one test for each modeling pitfall the notes list.

Example

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