The Data Space

Input data shared by every by-policy projection.

The five input CSVs are read here, once per model, and referenced from Projection as data. Projection is parameterized by point_id, so each Projection[N] is a separate ItemSpace with its own cells cache; if the readers lived there, every model point would re-read every file. Holding them in an unparameterized Space reads each file once no matter how many points are projected.

Inputs are external files: plain CSVs in the model folder’s parent directory, products/sofortrente/, rather than data stored inside the model. The model folder therefore holds nothing but formulas — no _data/, no IOSpec, no embedded values — so a diff of the model shows logic changes only. This follows annuallife.TradLife_A; contrast basiclife.BasicTerm_S, which keeps its inputs inside the model through modelx’s IOSpec machinery.

The consequence worth knowing: the model is not portable on its own. Copying the Sofort_DE_S folder without its parent’s CSVs produces a model that reads and then fails on first evaluation.

input_dir() resolves the directory from _model.path.parent at run time, so the model works wherever the repository is checked out. Each table has a filename Reference and a reader Cells:

Reference	Cells	File
model_point_file	model_point_table()	model_point_table.csv
mort_table_file	mort_table()	mort_table.csv
improvement_file	improvement_table()	improvement_table.csv
surplus_scale_file	surplus_scale_table()	surplus_scale_table.csv
hoechstrechnungszins_file	hoechstrechnungszins_table()	hoechstrechnungszins_table.csv

Every file but model_point_table.csv carries a final provenance column, one tag per row, per the library’s second ruling. A model point is a configuration rather than an assumption, and that is the only exemption.

The decrement tables are a [std] proxy, and here is its anchor

DAV 2004 R and DAV 2004 R-Bestand are the property of the Deutsche Aktuarvereinigung, are not public, and are not redistributed here. They are cited by name in sources.md and mort_table.csv ships a constructed proxy in their place, in four series — {FIRST, SECOND} x {M, F} — over attained ages 50 to 120:

q_base(x) = 1 - exp( -( A + B c^x (c - 1) / ln c ) ), A = 0.0002, B = 1.5e-5, c = 1.10 FIRST/M = 1.250000 x q_base(x) SECOND/M = 1.20 x FIRST/M FIRST/F = 0.795455 x q_base(x) SECOND/F = 1.20 x FIRST/F

q_base is the Gompertz-Makeham law the research file constructs and prints, with life expectancy 24,29 years at 65 and q(65) = 0.00789, q(75) = 0.02001, q(85) = 0.05078 — a prudent annuitant shape of the right order for a German first-order basis, and not DAV 2004 R.

The anchor is the unisex blend. The two sex factors are chosen so that the mix_male = 0.45 blend of the FIRST series reproduces q_base(x) itself: 0.45 x 1.250000 + 0.55 x 0.795455 = 1.00000025, the exact factor for the female series being 0.4375 / 0.55 = 0.79545454... and 0.795455 its six-decimal rounding. The blend therefore reproduces the research file’s own law to 2.5e-7 relative at every age, which is four orders of magnitude inside the tolerance any published figure is quoted to, and every annuity factor printed in _research/sofortrente.md can be traced into this model. Age 120 is the closing row: all four series are set to 1.0 there, so the survival path reaches zero inside the omega_age = 121 horizon.

improvement_table.csv carries the second half of the surface — a Trendfunktion proxy lambda_SECOND(x) = 0.0150 to age 70, tapering linearly to zero at 105, with lambda_FIRST = 1.25 x lambda_SECOND — and the model builds q(x, sex, cohort, basis) = q_table x (1 - lambda)^(cohort + x - mort_base_year) with mort_base_year = 2025, so the shipped tables are the period tables of calendar year 2025 and the exponent is the calendar year the life attains age x, less 2025. The exponent is negative for a cohort attaining an age before 2025 — an in-force point issued in 2012 reads pre-2025 mortality — and is not floored.

What a replacement must preserve. Three things, and a substitution that keeps only the first is not a substitution for this table. (i) The generational structure: a q(x, cohort) surface, not a period table, because a period proxy applied to a forty-year annuity understates the liability by a margin that dwarfs every other assumption. (ii) The first-order margin in both dimensions: lighter mortality (SECOND = 1.20 x FIRST) and a stronger improvement trend (lambda_FIRST = 1.25 x lambda_SECOND), because prudence in an annuity table must reach the rate of improvement as well as its level. (iii) The age-adjustment convention — here, integer attained age last birthday with the closing row at 120 — since a table supplied with an Altersverschiebung must have it applied before it is read here. Replacing the level alone leaves the wedge between the two bases wrong, and that wedge is the systematic Risikoüberschuss this product’s Überschussrente is largely financed from.

The other two assumption files are levels, not tables. surplus_scale_table.csv gives the opening Überschussrente share and its annual growth for each of the four Überschussverwendung forms, all [std]: no Überschussanteilsatz was established at any carrier for any year. hoechstrechnungszins_table.csv is the statutory rate history a model point’s tariff rate is checked against, by the contract’s own vintage — a German in-force book is a stack of cohorts and each carries its own cap.

Cells Descriptions

input_dir()

The directory holding the input CSVs: the model folder’s parent.

Inputs are external files, not data stored inside the model, so the model folder is pure formulas. The path is resolved at run time from where the model was read, following annuallife.TradLife_A.

model_point_table()

The model point table, read from model_point_table.csv.

Fourteen points, indexed by point_id. The only input file without a provenance column: a model point is a configuration rather than an assumption, and its columns are one contract’s own terms.

mort_table()

The annual death rates by basis, sex and attained age, from mort_table.csv.

Indexed by (basis, sex, age) with basis in {FIRST, SECOND} and sex in {M, F}. The unisex series the tariff is struck on is computed from these two at mix_male; it is deliberately not a row, because no real sex-distinct table carries one.

A [std] proxy, not DAV 2004 R; see the Space docstring for what it is, what its anchor is and what a replacement must preserve.

improvement_table()

The annual mortality improvement rates, from improvement_table.csv.

Indexed by (basis, age). This is the Trendfunktion of a generational table: the improvement lives inside the mortality surface, keyed by birth cohort, rather than being applied on top of a period rate keyed to the projection year. A [std] proxy; DAV 2004 R’s own trend is not public.

surplus_scale_table()

The Überschussverwendung scale by form, from surplus_scale_table.csv.

Indexed by surplus_form. surplus_init_pct is the Überschussrente at outset as a fraction of the garantierte Rente and surplus_growth its annual increase, for the four forms none / konstant / teildynamisch / volldynamisch.

Every figure is [std]. No Überschussanteilsatz was established for this product at any carrier for any year; what the corpus establishes is the shape — the constant form highest at outset and flat in intention only, the volldynamic form lowest at outset and rising with each declaration. The four forms are not calibrated to equal present value here, and a user who needs them to be must do that calibration.

hoechstrechnungszins_table()

The statutory Höchstrechnungszins history, from hoechstrechnungszins_table.csv.

Indexed by year_from, with year_to closing each band and max_rate the cap in force. A contract’s cap is the one in force at its own Vertragsbeginn and stays with it for life, so an in-force model point is checked against its vintage rather than against today’s rate. The cap is an upper bound and not the tariff rate: a carrier may price below it, and one in the corpus is observed doing so.