The FRV_DE_S Model

Reference liability cash flow model for the German fondsgebundene Rentenversicherung.

FRV_DE_S is the executable counterpart of products/fondsgebundene_rentenversicherung/technical-notes.md in the lifelib-products library. It projects gross best-estimate liability cash flows for a single-policy model point of a German unit-linked deferred private annuity — Schicht 3, single life, one fund, no Beitragsgarantie — over the *Aufschubzeit* only, on a monthly grid. At the end of month proj_len() - 1, the frame’s last, the units are cancelled, the Fondsguthaben is converted at the Rentenfaktor, and the contract leaves this model: the payout phase belongs to products/sofortrente/.

Three things make this the unit-linked model rather than a translated general-account one.

The insurer guarantees the number of units, not their value. There is no Rechnungszins in the accumulation phase, no Deckungskapital, no Zinsüberschuss and — because the Anlagestock holds the covering assets in the very units the liability is denominated in — no investment-mismatch term anywhere in the model. The state variable is units_pp(); euro are derived from it and a unit price. Every charge is either withheld from the Beitrag before units are bought or levied by cancelling units that already exist, and which of the two it is decides what happens when premiums stop.

``net_cf`` is the non-unit stream, and that is the model’s single most important convention. Every benefit paid before Rentenbeginn — the death benefit up to the fund, the Rückkaufswert, the Teilentnahme, the capital released at Rentenbeginn — is funded by cancelling the policyholder’s own units, so a gross presentation would count the same money twice. net_cf(t) is therefore charges collected, less insurer expenses, less the death strain. The gross flows are published beside it — premiums, prem_to_av, claims_death, claims_lapse, claims_maturity, withdrawals, av_releases are all result_cf() columns — and check_benefit_funding() asserts that they net exactly, so the exclusion is visible in the frame rather than merely asserted in prose.

Two mortality bases at once. The Risikobeitrag the tariff charges is priced on a death table (DAV 2008 T, first order); the projection decrements on the second-order best estimate. The wedge between them is the Risikoergebnis, and with the shipped flat mort_be_factor = 0.75 it is exactly 25 % of the Risikobeitrag collected. A model that uses one basis for both makes the risk result identically zero and deletes the mechanic. The Rentenfaktor rests on a third basis again — an annuity table, DAV 2004 R — which is why no cells reads both tables.

Spaces. The model contains two:

Data

Reads the six 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, which the contract forces rather than the modeller choosing: the dominant premium frequency is monthly, the kapitalbezogenen Verwaltungskosten and the Risikobeitrag are levied monthly by unit cancellation, and the Abschluss- und Vertriebskosten instalment runs for exactly 60 months. An annual grid cannot place the month-60 cliff, and that cliff is the characteristic shape of a German unit-linked contract’s early values. t is the 0-based policy month counted from the contract’s own inception — t = 0 is the inception month — so t = 60 means the same thing on every model point. The frame is range(proj_start(), proj_len()) with proj_start() = duration_init_m and proj_len() = 12 x (annuity_age - entry_age), the number of policy months and so the frame’s exclusive end; an in-force model point simply opens partway through it. The contractual policy year is the 1-based label t // 12 + 1.

What is sourced and what is not. The mechanics are common ground in German practice: the Beitragsverrechnung order, the five-year spreading of the acquisition charge, the Beitragsrückgewähr death benefit and its net amount at risk, the Zeitwert Rückkaufswert, the max(guaranteed, current) Rentenfaktor rule, and the survival of the fund-based charges into a beitragsfrei contract. The levels are almost entirely standardizations: no charge rate, no *Rentenfaktor*, no lapse rate and no expense loading was established at any carrier, and no document cited in this library was retrieved. The one anchor in the whole charge stack is the Höchstzillmersatz of 25 ‰ of the Beitragssumme, and the shipped tariff takes the cap rather than a guessed interior point. The DAV tables — DAV 2008 T for the risk charge, DAV 2004 R behind the Rentenfaktor — are the property of the Deutsche Aktuarvereinigung, are not public and are not redistributed here: they are cited by name and stood in for by anchored [std] proxies. This model is a mechanics demonstration, not a pricing, reserving or disclosure result. Nothing it produces may be quoted as an Effektivkostenquote or compared with a PRIIPs performance scenario, and its charge levels must be replaced with a real tariff before any quantitative use.

Model points. Thirteen, covering both premium forms, all four payment frequencies, an in-force cell opening at duration 96, a beitragsfrei cell on a zero-return fund, a Zuzahlung and a Teilentnahme, a Beitragsdynamik, a Nettotarif on an ETF, a two-year premium term inside a twelve-year deferment on a stress path, a cell with a non-zero Stornoabzug, and a Rentenbeginn at 70 where the current Rentenfaktor exceeds the guaranteed one so the max() bites. Model point 1 is the anchor cell of the worked example in the technical notes.

Verification. tests/test_fondsgebundene_rentenversicherung_de.py asserts the notes’ worked example to the cent and pols_if to six decimals, and one test per listed modeling pitfall. Seven check_*() cells travel with the model itself.

Example

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