The EC_FR_S Model

Reference liability cash flow model for French eurocroissance business.

EC_FR_S is the executable counterpart of products/eurocroissance/technical-notes.md in the lifelib-products library. It projects gross best-estimate liability cash flows for single-policy model points on the two composite chassis those notes specify — Chassis A, the 1° engagement carrying a provision mathématique alongside parts de provision de diversification, and Chassis B, the 2° engagement carrying parts only with a capital guarantee that bites at the échéance and nowhere before it.

Two provisions, two state variables, and one rebalancing a year — on a monthly grid. That sentence is the model. The provision mathématique is the guaranteed amount discounted at the A. 134-1 rate; the provision de diversification takes whatever the account’s assets leave over, floored at the parts’ minimum value. Neither is a cash flow. The policy’s cash flows are versements in and surrender, death and maturity claims out; the two provisions reach them only through the R. 134-5 surrender and R. 134-6 maturity formulas.

The provision mathématique is re-struck, never accumulated. pm(t) is mg(t) discounted at the current rate — i_pm(t + 1), the rate of the month’s own end-of-month striking, over the fractional remaining term — so it lands on the guarantee exactly at the échéance whatever the path of rates: in the last projected month the two are identically equal. That is what makes the Chassis A guarantee pre-funded by construction, and it is why an in-force model point carries no accumulated PM — the model re-derives it, and Projection.check_pm_restruck asserts the shipped extract agrees.

The Chassis B surrender value is not guaranteed. Before the échéance a 2° engagement pays parts × part value and nothing else. At the anniversary of the notes’ policy-year-6 shock — month t = 71 — that is 9,899.22 against a guarantee of 11,760.00 — 84.18% of net versements. A model that floors it is modelling a contract that does not exist, and that is this product’s central error. The monthly grid prices an exit on the striking of the month it falls in, as A. 134-5 requires, so a surrender in month 65 pays 11,430.63 instead.

The insurer’s own funds never reach a policyholder before the term. The L. 134-3 contribution completing the representation and the provision pour garantie à terme are computed, reported and kept out of every benefit column; Projection.check_own_funds_not_paid asserts it.

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, because A. 134-5 requires the diversification provision to be re-struck at an intermediate value at least monthly and prices an exit on a forward part value — the next striking after the request — which an annual grid can only standardize away. t counts policy months from issue and is 0-based: month t runs from time t to time t + 1, so t = 0 is the issue month. The frame is range(proj_start(), proj_len()) — proj_len() = 12 × policy_term() is the number of months projected, the last row is proj_len() - 1, and that row ends at the échéance. An in-force cell opens at proj_start() = 12 × duration_ifo, always the first month of a policy year. The initial versement is not a row of its own: it creates the rights and strikes both provisions as the opening state of the first projected month, reached as own_assets_at(t, "BOM") and its siblings. The contractual policy year is the derived 1-based label policy_year(t) = t // 12 + 1, and it is what the rachat table, the versement schedule, the lock-up and the apport are keyed by. Age is âge atteint and steps on the anniversary.

Assumptions stay annual and the grid underneath them gets finer. mort_rate(t), lapse_rate(t), wd_rate(t) and asset_return(t) are the annual figures the technical notes tabulate; mort_rate_mth(t), lapse_rate_mth(t), wd_rate_mth(t) and asset_return_mth(t) are what the month applies, 1 - (1 - q)^(1/12) and (1 + r)^(1/12) - 1, so twelve compound back to exactly the annual figure. Contractual terms stay where the contract puts them: the base 4° parts levy and a scheduled versement in the first month of a policy year; the striking of the compte de participation aux résultats, the base 5° performance levy on the year’s accumulated performance, the insurer’s asset affectations and any free versement on the anniversary, in that order. Both provisions are re-struck every month; the asset return accrues over the month; decrements and claims follow at its end.

What reconciles, and what does not. Because the monthly rates compound back to the annual ones and every contractual event sits on a year boundary, every anniversary-dated value — the assets, both provisions, the parts and their value, the guaranteed amount, the insurer’s own-funds items and every exit value — is exactly what the annual-step model this one replaced carried on the same row, to 1.3e-10 EUR across all eleven shipped model points, and pols_if(12k) is its opening in-force. The cash flows are not and are not meant to be: a claim falls at the end of the month of exit, maintenance expense accrues at one twelfth a month on the in-force and the provision of each month rather than of the anniversary, and on the one cell that takes rachats partiels the exit cash leaves in twelve instalments. Those timing differences are the reason for the finer grid, and technical-notes.md quantifies each of them.

What is sourced and what is not. The mechanics are sourced, and unusually completely so: eurocroissance is a statutory construct, and arts. L. 134-1 to L. 134-5, R. 134-1 to R. 134-12 and A. 134-1 to A. 134-7 of the Code des assurances fix the provision definitions, the six permitted charge bases, the surrender and maturity values, the minimum part value, the 90%-of-TEC discount ceiling and the PGT. Every rate is a standardization: no notice d’information, conditions générales or PRIIPs document d’information clé for any eurocroissance support was retrieved, the regulatory mortality tables are cited but never shipped, and no eurocroissance lapse experience is public. This model is a mechanics demonstration, not a pricing or reserving result.

Verification. tests/test_eurocroissance_fr.py asserts both chassis of the notes’ worked example row by row to the cent at the anniversary months — the asset roll, the parts levy and its base, the performance levy, the re-strike of the PM and its rate/time decomposition, the minimum part value, the insurer’s contribution, the PGT, the policy-year-3 versement split, and every exit value the two chassis pay — and the monthly claims the conversion added: that twelve monthly rates compound back to the annual ones, that no contractual event moves between anniversaries, and that the intermediate value is struck in every month.

Example

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