The Annuity_JP_A Model

Reference liability cash flow model for a Japanese fixed individual annuity.

Annuity_JP_A is the executable counterpart of products/individual_annuity/technical-notes.md in the lifelib-products library. It projects gross best-estimate liability cash flows for a single-policy model point of 定額個人年金保険 (teigaku kojin nenkin hoken, fixed individual annuity insurance) with the 税制適格特約 (zeisei tekikaku tokuyaku, tax-qualification rider) attached: a deferral phase in which a level office premium accumulates into the 保険料積立金 with a survivorship release, an annuitisation step at the 年金支払開始日, and a payout phase of 確定年金 (kakutei nenkin, annuity-certain) instalments — or, with the module switched on, 保証期間付終身年金 (a life annuity with a guarantee period).

The product is two contracts joined at one date, and the model is built that way. Before the 年金支払開始日 the liability is a savings fund with a death benefit capped at cumulative premiums and a surrender value capped at that; after it the liability is a stream of instalments that does not depend on survival at all. The two phases read different mortality tables — 生保標準生命表2018（死亡保険用）and 生保標準生命表2007（年金開始後用）— and the best-estimate adjustment to those tables reverses sign at the join, because the first is prudent against death and the second against longevity.

Spaces. The model contains two:

Data

Reads the seven 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 per model, 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. Annual steps, the notes’ base grid. t counts completed policy years since issue, 0-based: premiums fall at t = 0 .. m - 1, the fund accumulates over t = 0 .. n where n = m + d, and the annuity is paid at t = n .. n + k - 1. Premiums, annuity instalments, maintenance expense and commission fall at the start of the year; death benefits and surrender payments at the end; lapses act on the survivors of mortality, death before lapse. Acquisition expense and initial commission fall at t = 0. There are no tail states: the 確定年金 pays exactly k instalments and the contract ends.

What is sourced and what is not. The contractual mechanics are sourced: the death benefit as cumulative premiums, the surrender value capped at the death benefit, the unavailability of surrender from the 年金支払開始日, the unconditional 確定年金 instalments, and the published 年金の一括払 commutation factors. The mortality basis is not a published table. 標準生命表2018 and the 2007 年金開始後用 table are readable at stable public URLs but their publisher’s terms prohibit reproduction and transmission, so this library ships no copy of either: mort_table.csv is a [std] construction anchored to quoted spot rates — the canonical library-wide 死亡保険用 table graduated log-linearly between its sourced anchors, and a Makeham law on 年金開始後用 — and its provenance column says so on every row. The expense loading, the surrender charge, the lapse curve, the cash expenses and the best-estimate mortality factors are standardizations introduced for the reference implementation. This model is a mechanics demonstration, not a pricing or reserving result. Replace the assumption tables with company data, and the mortality basis with licensed tables, before drawing any conclusion from the output.

Model points. Nine. Point 1 is the anchor cell of the worked example in the technical notes and reproduces every figure it displays. The other eight exercise the female basis, a 15-year certain period, a zero 据置期間, the 保証期間付終身年金 election, full 年金の一括払 commutation, the 0.70 tontine death-benefit ratio, the 自動振替貸付 module, and the 契約者貸付 module run together with a non-zero declared dividend and dynamic lapse. Point 9 is the anchor cell with nothing changed but the payout form, so the ¥281,300 life-annuity instalment and the ¥638,100 certain one are bought out of the same 年金原資.

Verification. tests/test_individual_annuity_jp.py asserts the notes’ worked example — the annuitisation quantities, the four deferral rows, the fund and surrender value at the crossover, and the payout rows — to the precision the notes display, and every product fact the notes list as a modelling pitfall.

Example

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