Technical Notes#

Status: Draft, 2026-08-20 (all cited sources accessed 2026-08-20).

Scope note. These notes turn the standardized composite of product-spec.md (same directory) — endowment assurance (yōrō hoken, 養老保険) as the first cell and educational endowment (gakushi hoken, 学資保険) as the second — into a reference liability cash-flow projection on paper. This is not any single insurer’s product. [S#] and [R#] tags resolve against sources.md, whose numbering is carried verbatim from _research/endowment.md and is frozen; [REG-R#] tags resolve against the cross-product reference library references/regulatory-and-actuarial-references.md, whose own R-numbering is distinct. std marks a standardization introduced for the reference implementation; unverified marks a claim that could not be confirmed against a retrieved document. Every parameter value here is identical to product-spec.md’s. Eleven parameters appear here that the specification does not name, and every one of them is internal to a construction the specification defers to this document (its footnotes 6 and 21): the cash-value basis rate i_cv, the acquisition-deduction rate α, the mortality multiplier mort_be_factor, the waiver loading wv_load, the waiver-qualification fraction wv_frac, the waived-state surrender multiplier wv_lapse_mult, the surrender-rate table, the premium-default table, the dynamic-surrender sensitivity β, the expense and commission scale, and the reference valuation rate i_std. Each is std and each is derived, not asserted, below.

This product states deltas against the savings chassis. The policy value (hokenryō tsumitatekin, 保険料積立金), surrender value (kaiyaku-henreikin, 解約返戻金), policy loan (keiyakusha kashitsuke, 契約者貸付), automatic premium loan (jidō furikae kashitsuke, 自動振替貸付, APL), grace (yūyo kikan, 猶予期間), lapse (shikkō, 失効), reinstatement (fukkatsu, 復活) and reduction of the sum assured (gengaku, 減額) machinery is specified once, in whole life technical notes (終身保険), and is not restated here. Four things are genuinely this product’s and are given full treatment: a finite term with a 満期保険金 (manki hokenkin, maturity benefit) equal to the death benefit, which turns the policy-value roll-forward into a real check; a staged 学資金 (gakushikin, education money) schedule that is data rather than formula; a death payment (shibō kyūfukin, 死亡給付金) that is a return of premiums rather than a sum assured; and waiver of premium (hokenryō haraikomi menjo, 保険料払込免除) on the policyholder (keiyakusha, 契約者) — a second decrement on a second life who is not the 被保険者 (hihokensha, the insured). That last has no analogue in uslib or uklib.

Model scope and conventions#

  • Purpose. Project gross best-estimate liability cash flows per policy — premiums, death claims, staged survival benefits, the maturity benefit, surrender benefits, expenses and commission — for a single-policy model point, in the sense the ESR current estimate (genzai suikei, 現在推計) requires: probability-weighted future cash flows on assumptions re-set at each 基準日 REG-R15. They are gross of reinsurance, which is a scope choice of this library and not a requirement of that entry. It is also the shape the appointed actuary (hoken keirinin, 保険計理人) 1号収支分析 consumes — a forward income-and-outgo projection over at least ten future years by product segment, re-runnable under prescribed scenarios REG-R6 REG-R22. Discounting, MOCE, required capital and every statutory reserve are out of scope and are cited, not reproduced (see Valuation and reserve pointers).

  • Projection frequency. Annual, on policy years running anniversary to anniversary (Endowment_JP_A). The only intra-year contractual structure on the composite is the calendar date of each 学資金 — the 11月1日 following a stated attained age at the adopted carrier [S10], and four other fixed dates elsewhere [S1] [S3] [S7] [S13] — and the annual grid resolves every one of them to the policy anniversary following that age (product-spec.md footnote 13). No amount changes; the timing of each staged payment moves by between one and five months, always forward, always inside one policy year.

  • Timing conventions std. Premium at the start of each policy year, in advance, for years 1 … m; maintenance expense and renewal commission at the start of each year; acquisition expense and initial commission at issue (start of year 1); death claims and claim expenses at the end of the policy year of death; the 学資金 and the 満期保険金 at the end of the policy year, to policies surviving that year’s mortality; surrenders at the end of the policy year, after deaths and after any staged benefit due at that anniversary, valued on the surrender value net of that benefit.

  • Age basis — two ages, not one. 契約年齢 is attained age (man-nenrei, 満年齢) with the fractional year discarded at 契約日, incrementing on each 年単位の契約応当日 rather than on the birthday [S1] [S2] [S10] [S13]. The attained age of the 被保険者 in year t is therefore x + t − 1 exactly. On the 学資 cell there is a second age, the 契約者’s y + t − 1, which runs an entirely separate decrement over t = 1 … m only. Both model cells sit at exact integer ages at issue, so the four different 満年齢 rounding rules in the composite do not bind on either [S1] [S2] [S10] [S13]. The table does not share this basis: 生保標準生命表2018（死亡保険用）is built for a nearest-birthday (hoken-nenrei hōshiki, 保険年齢方式) basis REG-R20. The reference implementation reads it at the 満年齢 attained age with no adjustment std, as the chassis does, and the resulting understatement of up to half a year of age is named here, not hidden.

  • Currency. JPY throughout, written ¥ with thousands separators. There is no currency layer on this product.

  • Model points. Single-policy model points on an expected (probability-weighted) basis: survivorship multiplies per-policy cash flows. point_id parameterizes Projection; point_id = 1 is the 養老 worked-example anchor cell and point_id = 2 is the 学資 cell. No aggregation logic is specified here.

  • Termination — the sharpest delta from the chassis. There is no tail and no terminal age. The projection length is exactly the 保険期間: T = n. Every state closes at t = n, and the closing cash flow is a certain payment of S to the survivors, not a decrement. The chassis runs to the table’s terminal age ω because a 終身保険 has no expiry; importing ω here would project a contract that has already matured.

  • Contract boundary. The premium is level and guaranteed for the whole of 保険料払込期間 with no unilateral repricing right in any retrieved 約款 [S1] [S2] [S8] [S10], so all m years of premium and all n years of benefit are inside any defensible boundary. Japan’s ESR 柱1 告示 were not opened in the research pass and their boundary text is unverified REG-R16; the model implements no boundary test, projects the whole contract, and says so.

  • Rounding. Intermediate values at full precision; displayed cash flows to two decimal places std and in-force probabilities to six std, which is the precision the tests assert.

Model point attributes#

Attribute

Type

Anchor cell (point_id = 1)

Second cell (point_id = 2)

policy_id

str

EN-JP-0001

EN-JP-0002

cell

enum {endowment, education}

endowment

education

sex

enum {M, F}

M

M

issue_age (x)

int, 満年齢 — the 被保険者

30

0

ph_issue_age (y)

int, 満年齢 — the 契約者; unused on the 養老 cell

—

30

ph_sex

enum {M, F}

—

M

sum_assured (S)

JPY — 基準保険金額

5,000,000

1,000,000

policy_term (n)

int years

30

22

prem_term (m)

int years, m ≤ n

30

17

premium_annual (P)

JPY, level for years 1 … m

181,140

108,564

schedule_id

str — key into benefit_schedule_table.csv

none

S_0_1

waiver

bool — 保険料払込免除 on the 契約者

false

true

apl_elected

bool — 自動振替貸付 elected (default on)

true

true

pol_loan_util

fraction of cv_pp drawn as 契約者貸付

0.00

0.00

dividend_type

enum {none, five_year}

none

none

apl_default_mult

multiplier on default_rate(t); 0 switches the APL module off

0.00

0.00

dyn_lapse

bool — dynamic-surrender module

false

false

mort_adj, wv_load, wv_frac, wv_lapse_mult

the four class-(c) multipliers, carried per point; the mort_adj column is read by the mort_be_factor() cells

1.00

1.00

Both annual premiums are sourced, not constructed. ¥15,095 per month for exactly the anchor cell — 契約年齢 30, 満期 60, 保険金額 ¥5,000,000, male, contracts dated on or after 2025-01-02 — is published [S9], and ¥9,047 per month for exactly the second cell — 契約者 30 male, child 0, 22歳満期, 17-year paying period, 満期保険金 ¥1,000,000, S型 — is published with its total premiums and receipts [S11]. The annual figure is 12 × the monthly one std (product-spec.md footnote 5): 12 × ¥15,095 = ¥181,140 and 12 × ¥9,047 = ¥108,564, the latter reconciling to the published ¥1,845,588 of total premiums over 17 years exactly [S11]. No carrier publishes an annual-mode scale, so the modal discount a real 年払 rate would carry is not applied and both annual premiums are slightly overstated. The direction matters more here than on the chassis, because the number this product is sold on moves with it: one carrier states plainly that paying in larger blocks lowers total premiums and raises the return ratio (henreiritsu, 返戻率) [S16], and the highest published ratio in the research set, 129.2%, is quoted on a 一括払込 basis [S14]. The model’s derived 返戻率 is therefore a monthly-basis ratio evaluated on an annual grid and sits below a true 年払 figure.

schedule_id = none on the 養老 cell is a product fact, not a missing value: the survival benefit is a single payment at t = n and there is no staged schedule at all.

State variables#

Variable

Description

Updated

pols_if(t)

Total in-force probability at the start of policy year t, pols_if = pols_if_pay + pols_wv; pols_if(1) = 1

sum of the two states

pols_if_pay(t)

In-force probability in the premium-paying state at the start of policy year t; pols_if_pay(1) = 1

annual recursion

pols_wv(t)

In-force probability in the waived state at the start of year t; pols_wv(1) = 0; identically 0 on the 養老 cell

annual recursion

mort_rate(t)

被保険者 mortality (incl. 高度障害) in year t

table lookup at x + t − 1

mort_rate_ph(t)

契約者 mortality driving the waiver, t ≤ m only; 0 on the 養老 cell

table lookup at y + t − 1

lapse_rate(t)

Voluntary surrender rate in year t

assumption table

default_rate(t)

Premium-default rate feeding the APL module (0 in base)

assumption table

benefit_pct(t)

g(t) — the staged benefit due at anniversary t, as a fraction of S

schedule table

pol_val_pp(t)

W(t) — policy value at anniversary t, after any staged benefit due at t

closed form

pol_val_pre_pp(t)

Wb(t) = W(t) + S × g(t) — the same value before that benefit

closed form

surr_charge_pp(t)

SC(t) — the acquisition deduction embedded in the surrender value

closed form

cv_pp(t)

CV(t) — payable 解約返戻金 at anniversary t

closed form

reserve_pp(t)

平準純保険料式 policy reserve, reference quantity only — never a cash flow

closed form

loan_pp(t, s)

Outstanding APL + 契約者貸付 principal and interest, by entry year s

chassis recursion

The base run carries no loan and no APL cohort: default_rate ≡ 0 and pol_loan_util = 0, so loan_pp ≡ 0 and every benefit is gross. The APL triangle, its exhaustion test and its clawback are the chassis’s and are exercised in both positions there.

There is no low_cv and no k. No retrieved document offers a suppressed-surrender-value (tei-kaiyaku-henreikin-gata, 低解約返戻金型) form of either product; the one appearance of the term in the research set is on a different product group in a pricing release [S9]. The chassis’s signature mechanic — the cliff at 払込満了 and the surrender spike on it — is absent by construction here, and so is the lapse-rate spike that goes with it.

Assumption inputs#

Three classes, kept apart on purpose. The split is not a modelling nicety on this product: the 返戻率 an insurer advertises is a ratio of guaranteed receipts to guaranteed premiums on a 無配当 design [S13] [S16] but a partly non-guaranteed one on a 有配当 design [S1] [S6] [S10], and presenting a non-guaranteed element as certain is 断定的判断の提供 under 消費者契約法第4条 REG-R38.

(a) Contractual / guaranteed elements (cited; the insurer cannot change them)#

Input

Value

Basis

死亡保険金 — 養老 cell

S, level for the term, net of loans and unpaid premiums

[S2] [S8]

満期保険金 — 養老 cell

S on survival to t = n, equal to the death benefit

R10 [S2] [S8]

高度障害 / 重度障害 — 養老 cell

Deemed death on the notice date; no separate payment

[S2] [S15]

Premium P

Level and guaranteed for years 1 … m; none thereafter

[S1] [S2] [S8] [S10]

Staged 学資金 g(t)

5% / 5% / 10% / 10% / 70% / 10% of S at t = 3 / 6 / 12 / 15 / 18 / 20

[S10] [S11]; grid std, timing std

満期保険金 — 学資 cell

S at t = n = 22; total receipts 210% of S

[S10] [S11]

死亡給付金 — 学資 cell

max(cumulative premiums − 学資金 already paid − loans, 積立金)

[S3] [S13]; form std

保険料払込免除 trigger

The 契約者’s death, 高度障害, or 身体障害 from a listed accident within 180 days, during 保険料払込期間

[S1] [S10] [S16]

What the waiver promises

Every benefit paid in full and each future premium treated as paid on its 契約応当日

[S1] [S10] [S13]

Waiver carve-outs

3-year suicide of the 契約者; the 後継保険契約者’s intentional act; war — each terminating the contract against the policy reserve (sekinin-junbikin, 責任準備金)

[S1] [S3] [S7] [S10]

解約返戻金 arguments

Elapsed months, capped at paid months, and the timing of the 学資金 payments

[S1] [S2] [S10]

解約返戻金 constraints

Below cumulative premiums; capped at the death benefit; reduced by each 祝金

[S7]

免責 — suicide of the 被保険者

3 years from the 責任開始の日, paying the 積立金 or 責任準備金 rather than nothing

[S2] [S8]; frame REG-R34

Contestability (告知義務違反)

2 years from the 責任開始期, on the 契約者’s disclosure as well as the 被保険者’s

[S1] [S6]; ceiling REG-R35

Policyholder protection

90% of the 責任準備金 on insurer failure

REG-R40 REG-R41

(b) Insurer-discretionary current elements#

Input

Snapshot value

Basis

Assumed interest rate — the pricing rate (yotei riritsu, 予定利率)

1.00% p.a. on both cells, for contracts dated on or after 2025-01-02 (学資保険 0.85% → 1.00%; 養老保険（一時払を除く）0.60% → 1.00%)

[S9]; adoption std

Cash-value basis rate i_cv

1.00% p.a. — the 予定利率 above, adopted directly

[S9]; adoption std, below

Acquisition deduction α

0.25 of one annual premium, grading linearly to zero at m

std, below

APL / 契約者貸付 interest i_L

2.40% p.a., compound, held flat — a named deviation from the chassis’s 2.75%, below

[S9]; ceilings 年8% / 半年4% [S1] [S10]

契約者配当

None — the composite is 無配当. The ５年ごと配当 variant is specified and not implemented: dividend_type is an attribute and the value is rejected by name

[S13] [S16]; variant [S1] [S10]; frame REG-R9

Deferral of paid 学資金

Not modelled: each 学資金 is paid on its due date at a rate no document publishes

[S1] [S10] [S13]; scope std

払済保険 / 学資年金 commutation

Not modelled in the base run; both need an unpublished company basis

[S7] [S10]

減額

Universal and specified in product-spec.md, not modelled: it is the chassis’s mechanic, and on the 学資 cell it re-scales the whole staged grid because every payment is a percentage of 基準保険金額. One carrier refuses it once the 学資年金開始日 has arrived

[S1] [S2] [S6] [S10]; scope std

Why i_cv is the 予定利率 here, and why that is better than the chassis could manage. On the whole-life chassis the pricing rate had to be solved out of a published surrender-value table, because no carrier published the rate. On this product the position reverses: no carrier publishes a surrender-value formula or a numeric surrender-value table for either cell — a sharper gap than the chassis’s [S1] [S2] [S10] REG-R2 — but one carrier publishes the 予定利率 by name, by product group, before and after a dated revision, and it is 1.00% for both product groups in the same release [S9]. So the library adopts the published rate as the cash-value basis and derives the loading rather than the rate. Adopting it is the standardization; the number is sourced. The other legs of the basis stay dark: the 予定死亡率, the 予定事業費率 and the surrender-value formula sit in the 保険料及び責任準備金の算出方法書, a filed but unpublished 基礎書類 under 保険業法第4条第2項 REG-R2.

What the loading then is — a derived output, and a seam that shows. With i_cv = 1.00% and the male valuation table, the net level premium on the anchor cell is π = ¥145,896.34 against a sourced gross premium of ¥181,140, an implied loading of ¥35,243.66, or 19.457% of the gross premium. That is a plausible number for a 30-year endowment, and it is coherent because the premium and the rate come from the same carrier and the same release [S9]. On the second cell the same calculation gives π_g = ¥110,458.94 against ¥108,564 — a loading of −1.745%, which no real product carries. The reason is the composite’s seam: that premium is a different carrier’s [S11] and that carrier does not publish its 予定利率. Restated as rates rather than loadings, the two cells’ guaranteed cash flows imply internal rates of −0.4239% on the 養老 cell and +1.1592% on the 学資 cell. Both are derived diagnostics, both are printed by the model, and neither is an input.

Why i_L is 2.40% where the chassis sets 2.75% — a named deviation, not an oversight. The mechanic is the chassis’s and is not restated here; the rate is not the chassis’s, and that is deliberate. The chassis picks 2.75% off one carrier’s vintage 貸付利率 schedule — the band a contract written under the older 予定利率 falls in — and marks the pick std. On this product a carrier publishes its 契約貸付利率 by name and by vintage, 2.00% → 2.40% for contracts dated on or after 2025-01-02, in the same release that moved the 予定利率 to 1.00% [S9]. Taking 2.40% keeps the loan rate and the pricing rate on one document and one vintage, which is worth more here than agreement with the chassis — and the two are not required to agree, for the reason both sets of notes give: the loan rate tracks the contract’s own vintage 予定利率, not the market, so a 終身保険 written on a different 予定利率 carries a different loan rate by construction. What the two products do share is the 約款 ceiling, 年8% / 半年4% [S1] [S10]. The rate is unused in the base run in any case; it binds only on model points 8 and 9.

α, and why it is re-based on premium. The chassis expresses the acquisition deduction as α × SA × max(0, m − t) / m with α = 0.0090, calibrated against a published table. That form is meaningless on the 学資 cell, where 基準保険金額 is a benefit-scaling unit and not a sum assured — total premiums are 1.85 times it. The deduction is therefore re-based on one annual premium std:

SC(t) = α × P × max(0, m − t) / m,     α = 0.25

On the anchor cell that is SC(0) = ¥45,285, within 0.7% of the ¥45,000 the chassis calibrated against a real published surrender-value run — so the only piece of genuine Japanese surrender-value calibration in this library is carried across rather than discarded. The construction satisfies the three sourced quantitative constraints [S7]: the value is below cumulative premiums at every duration on both cells (rising monotonically to 92.0% at t = n on the 養老 cell; on the 学資 cell the ratio saw-tooths with the schedule, peaking at 98.4% at t = 11 — the year before the third 学資金 — and standing at 94.2% at t = m), it is capped at the death benefit, and each 学資金 reduces it. It does not reproduce the fourth, adjectival, constraint — that the early durations return “either nothing at all or very little” [S7]: CV(1) is 55.4% of the first year’s premium on the anchor cell. α is the named lever and this is listed as a model risk.

(c) Behavioral / experience assumptions (modeler’s view)#

Mortality — two lives, one table, opposite margins. 生保標準生命表2018（死亡保険用）is the sourced basis on both lives, read from the publisher’s own PDF REG-R18 R1. It includes 高度障害 inside the death rate REG-R20 R2, so the 養老 cell’s 重度障害 benefit is not a separate decrement. It is a valuation table: 2008/2009/2011 experience, an improvement allowance, then a 数学的危険論による補整 sized to roughly a 2σ level R2 REG-R20 — so a best-estimate basis is a std adjustment of a sourced table.

Input

Value

Basis

Base table — male

生保標準生命表2018（死亡保険用）男, at attained age; both worked-example cells are male

REG-R18 R1

Base table — female

生保標準生命表2018（死亡保険用）女, at attained age, built from its own sourced anchors — never derived from the male column

REG-R18 R1

Interpolation between sourced ages

Log-linear in ln q, rounded to 5 decimals — the table’s own granularity

std

mort_be_factor (被保険者)

1.00 in the base run

std

wv_load (契約者, waiver)

1.00 in the base run

std, below

wv_frac

1.00 — every 契約者 death qualifies for the waiver

std, below

Improvement overlay

None

std

mort_be_factor = 1.00 means the base run is a valuation-table run, not a best estimate, taken so that every number in the worked example can be checked against a document anyone can download. The IAJ’s site terms prohibit reproduction and transmission without written consent REG-R21, so jplib cites the table by URL, quotes the individual rates its worked example needs, and ships mort_table.csv as a std construction whose provenance column points at the IAJ entry REG-R18 row by row.

mort_table.csv is the library-wide canonical construction, identical row for row in every jplib product that ships it, so one cell carries one value and one provenance string wherever it appears. Every row says which of two things it is: an ANCHOR row is a rate read from the published table and quoted under attribution, and an INTERPOLATED row is the log-linear fill in ln q between the two neighbouring anchors, rounded to five decimals. There is no extrapolation: both sexes run from an age-0 anchor upward, so every non-anchor age lies strictly between two sourced anchors.

Both sexes are built the same way, each from its own anchors. There is no ratio, no sex multiplier and no derivation of one column from the other — the female rates are the published female rates at the anchor ages and the same interpolation between them. Over the ages this product reads, the male anchors are 0, 1, 3, 5, 10, 15, 17, 18, 20, 22, 25, 30, 31, 32, 33, 34, 35, 40, 45, 50, 55 and 60, and the female anchors the same list without 31 to 34. Neither worked-example cell reads the female column; model points 5 and 6 are the only ones that do.

The file is restricted to attained ages 0 to 60, which is every age these nine model points reach: the oldest, the 養老 anchor cell, matures at attained age 60.

The margin points in opposite directions on the two lives, which is why they are two inputs. On the 契約者 the waiver is a cost, so a table that overstates mortality overstates the liability and is prudent. On the 被保険者 child the death benefit is approximately the reserve the contract already holds, so the same margin is nearly neutral — q runs 0.00081 at age 0, 0.00022 at 3, 0.00010 at 10, 0.00046 at 18 and 0.00066 at 22 on the male table R1 REG-R18, and the whole 22-year child decrement contributes ¥4,120.71 of claims against ¥1,521,101.61 of premium income on the second cell. One projection carrying a margin that is conservative on one life and neutral on the other is a reason to hold two mortality inputs rather than one basis. The freely redistributable 第23回生命表 is the benchmark against which the margin can actually be sized REG-R24.

wv_load is the one place a separate disability decrement is right. The table already carries 高度障害 REG-R20, so the waiver’s death and 高度障害 triggers are inside q. The third trigger — 身体障害 from a listed accident within 180 days, present at three of the six carriers [S1] [S10] [S16] — is not. wv_load is the multiplier that would add it; it is 1.00 in the base run std because no retrieved source gives an incidence, and holding it at 1.00 therefore understates the waiver. That is the exact opposite of the chassis’s ruling on 高度障害, where adding a decrement double-counts, and confusing the two is a pitfall.

wv_frac, and what a carve-out actually does. When the 3-year suicide carve-out, the successor’s intentional act or war bites, the contract does not merely lose the waiver — it terminates, paying the 責任準備金 to the 契約者’s legal heirs [S1] [S7] [S10]. wv_frac = 1.00 std in the base run because no retrieved source gives a suicide incidence by duration for Japanese lives; the 1 − wv_frac path exists, is wired, and produces the claims_ph_death column, which is identically zero in the base run. That zero is a product fact worth publishing, in the same way claims(t, "LAPSE") is on the UK term chassis.

Surrender. No carrier publishes a lapse or surrender curve by duration for either product; this is the single largest assumption gap. The only public benchmark is the industry 解約・失効率 of 5.6% for FY2024, defined as surrendered-and-lapsed sum assured over opening in-force sum assured, industry-wide across all product types R9 REG-R31 — an amount-weighted, all-product bound used here as a sanity ceiling and nothing more.

Policy year t

1

2

3 … n−1

n

lapse_rate(t) std

4%

3%

2%

0%

On the waived state the same table applies, multiplied by wv_lapse_mult = 1.00 std. The premium-default rate u(t) that feeds the APL module sits in the same table and is 1.0% / 0.8% / 0.6% std on the same 1 / 2 / 3-onwards shape, gated to zero in the base run by apl_default_mult = 0. No retrieved document gives a default rate for either cell, so it too is inherited from the chassis for the same comparability reason.

The 4 / 3 / 2 shape is inherited from the chassis so that the two products stay comparable. Two deltas. First, there is no cliff and therefore no spike: the chassis’s 17% at t = m exists only because a 低解約返戻金型 surrender value steps up by 1/k at 払込満了, and neither cell has one. Second, lapse_rate(n) = 0 std: a surrender at the end of the final policy year and the maturity payment fall on the same anniversary, and an owner one year from a guaranteed S does not take CV(n) = S early. Setting it to anything else double-counts the terminal payment. wv_lapse_mult = 1.00 is a placeholder that is almost certainly too high — a waived policy receives every benefit for no further premium and has a strictly dominant reason to persist — and it is named so that it can be moved.

Expenses and commission (levels all std; no carrier publishes an expense basis at all — 予定事業費率 is named in the 保険契約者保護機構 boilerplate and never quantified). Inherited unchanged from the chassis so that the products stay comparable:

Input

Value

Acquisition expense E0

¥50,000 per policy at issue std

Initial commission c0

90% of the annual premium at issue std

Renewal commission c_r

3% of premium, years 2 … m, on the premium-paying state only std

Maintenance expense e(t)

¥8,000 p.a. to t = n, inflating at 1.0% p.a., on both states std

Claim expense ec

¥20,000 per death claim std

Maturity and staged-benefit expense

None — folded into maintenance std

Renewal commission on the paying state only and maintenance on both is not a detail: a waived policy costs the insurer administration and pays the distributor nothing.

Cash flow components and recursions#

Notation (defined once, used throughout)#

Symbol

Meaning

t

policy year, t = 1 … n; the 被保険者’s attained age in year t is x + t − 1

x, y

契約年齢 of the 被保険者 and of the 契約者 (学資 cell only)

n, m

保険期間 in years; 保険料払込期間 in years, m ≤ n

S, P

基準保険金額; annual premium, payable at the start of years 1 … m

g(t)

staged 学資金 due at anniversary t, as a fraction of S; 0 on the 養老 cell

G(t)

Σ_{s ≤ t} g(s) — cumulative staged fraction paid to and including t

q(t), q_p(t)

被保険者 mortality in year t; 契約者 mortality in year t, zero for t > m

w(t), u(t)

voluntary surrender rate; premium-default rate (APL module)

l(t)

total in-force probability at the start of year t (pols_if), l = l_p + h — the same l the 終身 and 外貨建 chassis use, where there is only one state

l_p(t), h(t)

in-force probability in the paying state (pols_if_pay) and the waived state (pols_wv)

D(t), Dp(t)

expected 被保険者 deaths in year t; expected 契約者 decrements in year t

R(t)

expected in force at the anniversary, after mortality, before surrender

Sr(t)

expected surrenders in year t

A(z, k), ä(z, k)

k-year endowment-assurance EPV of 1 at age z; k-year annuity-due, both on i_cv and the table

π, π_g

net level premium on the cash-value basis, 養老 cell and 学資 cell

W(t), Wb(t)

policy value at anniversary t, after and before the staged benefit due at t

SC(t), V(t), CV(t)

acquisition deduction; ordinary surrender value; payable 解約返戻金

DB(t)

death benefit for a death in year t

L(t)

loan + APL principal and interest at the start of year t

i_cv, i_L, i_std

cash-value basis rate; loan rate; reference valuation rate

α

acquisition-deduction rate, per unit of one annual premium

E0, e(t), c0, c_r, ec

acquisition expense; maintenance; initial and renewal commission; claim expense

CF(t)

net cash flow of year t, income-positive (net_cf)

ρ

返戻率 — the derived return ratio (below)

Dimensional check. q, q_p, w, u, g, G, α, c0, c_r, l, h and ρ are dimensionless, and so are l_p and q_p; i_cv, i_L, i_std are per annum; A and ä are pure numbers (ä in years of premium, so S × A / ä is ¥ per year); S, P, W, Wb, SC, V, CV, DB, L, E0, e, ec are ¥; every term of CF(t) is ¥ per policy issued per year. g(t) is a fraction of S, never of a premium — the two are within a factor of two of each other on the second cell, so the check is not idle.

The staged schedule is data#

g(t) is read from benefit_schedule_table.csv, keyed by schedule_id, one row per payment, with a provenance column on every row:

schedule_id   t   benefit_pct   provenance
S_0_1         3   0.05          S型 grid, child 契約年齢 0-1 [S10]; timing [std]
S_0_1         6   0.05          "
S_0_1        12   0.10          "
S_0_1        15   0.10          "
S_0_1        18   0.70          "
S_0_1        20   0.10          "
J            18   1.00          J型 degenerate variant [S10]; timing [std]

The 満期保険金 of 100% at t = n is not a schedule row: it is always present, on both cells, and is held separately so that a schedule with no rows at all still matures. The observed designs run from a single 100% payment [S10] through three 20% 祝金 plus a five-instalment 学資年金 [S7] to four equal payments of 100% each [S13], so any implementation that hard-codes a shape is modelling one carrier. The J row is retained precisely because a grid that collapses to two payments is the sharpest test that the schedule is data.

The two policy-value constructions#

They differ because the two products insure different things, and the difference is not cosmetic.

養老 cell — an endowment assurance, so the death benefit is inside the EPV.

π      = S × A(x, n) / ä(x, m)
W(t)   = S × A(x + t, n − t) − π × ä(x + t, max(m − t, 0))
Wb(t)  = W(t)                                        (g is identically zero)
DB(t)  = S − L(t)

where A(z, k) is the k-year endowment assurance — 1 at the end of the year of death within k years, or 1 on survival to k. At t = n, A(x + n, 0) = 1 and ä(·, 0) = 0, so W(n) = S exactly, by construction. That identity is why the 養老 cell is a better test of a savings model than the chassis is: a whole-life reserve that drifts can hide for decades, while an endowment reserve that does not converge on its own maturity benefit is wrong on the first run.

学資 cell — survival benefits only, because the death benefit releases the value.

EPV(t) = S × [ Σ_{s > t} g(s) · v^(s−t) · (s−t)p_(x+t)  +  v^(n−t) · (n−t)p_(x+t) ]
π_g    = EPV(0) / ä(x, m)
W(t)   = EPV(t) − π_g × ä(x + t, max(m − t, 0))
Wb(t)  = W(t) + S × g(t)
DB(t)  = max( P × min(t, m) − S × G(t − 1) − L(t),  Wb(t) )

The Σ_{s > t} is what makes W(t) the value after the staged benefit due at t, which is the sourced fact that each 祝金 reduces the surrender value [S7] and that one carrier computes the value from the elapsed months and the 学資金 timing [S1]. Excluding the death benefit from the EPV is the std step, and it is one carrier’s own wording read literally: its 死亡払戻金 is the 責任準備金相当額 [S10], so on that design the decrement is exactly value-neutral, and the composite’s max-form dominates it [S3] [S13]. At t = n there is no future staged benefit and no future premium, so W(n) = S exactly here too.

Then, on both cells,

SC(t) = α × P × max(0, m − t) / m
V(t)  = max(0, W(t) − SC(t))
CV(t) = V(t)

with no 低解約返戻金型 multiplier: CV and V are the same series on this product.

The premium term in DB(t) is deemed-paid, not cash-paid. P × min(t, m) counts every premium falling due to t, whether or not the 契約者 was alive to pay it, because the waiver provides that each future premium is treated as having been paid on its 契約応当日 [S1] [S10] [S13]. The same wording is why CV(t) is identical in both states: the surrender value is computed as if the premiums had been paid, so the waived and paying states share one policy value. A model that keeps two value series is modelling a contract nobody wrote.

The waiver as a state transition, not a benefit#

W(t) is the reference quantity for the reserve; the waiver produces no outgo line at all. What it produces is the absence of premium income, which is why it can be omitted without any claim column looking wrong. On the 学資 cell, for t = 1 … n:

q_p(t)        = 0  for t > m                          (no premium left to waive)
l(t)          = l_p(t) + h(t)                         (total in force)
D(t)          = l(t) × q(t)                            (被保険者 deaths, both states)
Dp(t)         = l_p(t) × (1 − q(t)) × q_p(t)            (契約者 decrements, paying only)
to waived     = wv_frac × Dp(t)
terminating   = (1 − wv_frac) × Dp(t)                 (pays Wb(t) to the heirs)

l_p_after(t)  = l_p(t) × (1 − q(t)) × (1 − q_p(t))
h_after(t)    = h(t) × (1 − q(t)) + wv_frac × Dp(t)
R(t)          = l_p_after(t) + h_after(t)

l_p(t + 1)    = l_p_after(t) × (1 − w(t))
h(t + 1)      = h_after(t) × (1 − wv_lapse_mult × w(t))

The two lives are independent std — no retrieved document gives a dependency and none could. Where the 契約者 is the child’s parent, common-accident dependence is real and unmodelled.

q_p(t) = 0 for t > m is a modelling ruling and earns its own sentence. The 約款 make every waiver trigger conditional on the event falling during 保険料払込期間 [S1] [S10], and the termination-without-waiver path is the failure mode of that same provision [S1] [S7] [S10]. After 払込満了 there is no premium to waive and nothing for the provision to fail at, so the composite std treats the contract as continuing through the 契約者’s death by succession [S1] [S7] [S10] [S13] and drops the second decrement entirely. On the second cell that covers five years of the 22-year term — the years in which 86% of the receipts fall — and carrying the decrement through them would terminate a further 0.8367% of policies and delete their maturity benefits.

Processing order (policy year t = 1 … n)#

  1. Start of year — premium. Collect P × l_p(t) if t ≤ m — on the paying state alone, never on l(t). The waived state is in force and pays nothing. On an APL cohort the premium is not collected in cash: the advance is applied to it and it appears only as growth in L (chassis).

  2. Start of year — expenses and commission. e(t) × l(t), on the whole in force; renewal commission c_r × P × l_p(t) for 2 ≤ t ≤ m, on the paying state only. At t = 1 additionally E0 and c0 × P.

  3. Start of year — APL test (module on). Chassis, unchanged, run against CV.

  4. Values. Compute W(t), Wb(t), SC(t), V(t), CV(t) at the year-end anniversary.

  5. End of year — 被保険者 deaths. D(t) = l(t) × q(t), on the whole in force; outgo DB(t) × D(t), floored at zero; claim expense ec × D(t).

  6. End of year — 契約者 decrement, on the paying state only and only for t ≤ m: split by wv_frac into a transition to the waived state and a termination paying Wb(t).

  7. End of year — staged benefit. S × g(t) × R(t), to everything in force at the anniversary, in both states. It is not a decrement and it terminates nothing.

  8. End of year — maturity, at t = n only. S × R(n).

  9. End of year — surrenders, on survivors of both mortality decrements, valued on CV(t) — that is, net of the staged benefit just paid: `Sr(t) = l_p_after(t) × w(t)

    • h_after(t) × wv_lapse_mult × w(t); outgo max(0, CV(t) − L(t)) × Sr(t)`.

  10. Loan roll-up and in-force update per the chassis, then l_p(t+1) and h(t+1) above.

  11. At t = n everything closes: l(n + 1) = l_p(n + 1) = h(n + 1) = 0. There are no tail states.

Net cash flow#

Income-positive, per policy issued:

CF(t) = P × l_p(t) × 1{t <= m}                        (premiums)
      − DB(t) × D(t)                                  (被保険者 death claims)
      − ec × D(t)                                     (claim expense)
      − Wb(t) × (1 − wv_frac) × Dp(t)                 (契約者 death, waiver refused)
      − S × g(t) × R(t)                               (staged 学資金)
      − S × R(n) × 1{t = n}                           (満期保険金)
      − max(0, CV(t) − L(t)) × Sr(t)                  (surrender benefits)
      − e(t) × l(t)                                   (maintenance expense)
      − c_r × P × l_p(t) × 1{2 <= t <= m}             (renewal commission)
      − (E0 + c0 × P) × 1{t = 1}                      (acquisition)

net_cf is income-positive throughout; where an outgo-positive orientation is printed it survives as liability_cf, with net_cf(t) == −liability_cf(t). The result columns are premiums, claims_death, claims_staged, claims_maturity, claims_lapse, claims_ph_death, expenses, claim_expenses, commissions and net_cf, with pols_if first, then pols_if_pay and pols_wv beside it. claims_staged and claims_ph_death are named for the kind arguments "STAGED" and "PH_DEATH" that produce them.

expenses is the policy expense and nothing else. The expenses column carries E0 and e(t); the claim handling expense ec × D(t) is a per-claim cost, not a per-policy one, and it is published as its own claim_expenses column and deducted explicitly in CF(t) above. The worked example below therefore prints the two as two columns.

Roll-forward identity. Every policy leaves by exactly one route and the term is finite:

Σ_t D(t) + Σ_t (1 − wv_frac) × Dp(t) + Σ_t Sr(t) + R(n) = 1,   and   l(n+1) = 0

check_pols_roll_fwd() takes no argument and returns a bool over all t; the per-t signed residual lives at check_pols_roll_fwd_resid(t). A second check has no analogue on the chassis: check_pol_val_terminal() asserts pol_val_pp(n) == sum_assured to the displayed precision, on both cells.

返戻率 as a derived output#

The number both products are sold on is a ratio of contractual amounts on one policy that survives, pays every premium, takes every benefit in cash and receives no dividend — not a probability-weighted quantity, not discounted, not net of tax:

ρ = ( S × Σ_t g(t) + S ) / ( P × m )

henreiritsu() is a cells with no argument returning ρ. On the anchor cell ρ = 5,000,000 / 5,434,200 = 92.0099%; on the second cell ρ = 2,100,000 / 1,845,588 = 113.7849%, against the “approx. 113.7%” the carrier publishes for exactly that plan [S11] — the carrier truncates rather than rounds. Four things must be said about it, and all four are testable:

  • It is not a rate of return. Restated as one, the anchor cell’s guaranteed cash flows imply −0.4239% p.a. and the second cell’s +1.1592% p.a.

  • It is undefined on a policy that surrenders, and it is not the ratio the model’s own cash-flow statement produces, which is probability-weighted and carries expenses.

  • It is unbounded on a waived policy, where the denominator stops growing and the numerator does not — which is why henreiritsu() reads the contractual premium term P × m and never the projected premium income.

  • It moves with payment frequency and volume band [S13] [S14] [S16], so a ratio computed from a 月払 premium on an annual grid is a lower bound on the carrier’s own figure.

Policyholder behavior modeling#

All dynamic forms are std reference constructions; no public calibration evidence exists for any of them on either product.

  • Base surrender. The duration table in class (c): flat 2% from year 3, no cliff and no spike, and zero in the final year.

  • The waived state is not a lapse state. There is no premium to miss, so the premium-default decrement u(t) and the APL do not run there at all; only voluntary surrender and the 被保険者’s death can end a waived policy before maturity. Applying a premium-default decrement to the waived state models a decrement the contract does not have.

  • Premium default and the APL. Chassis, unchanged: a decrement out of the paying cohort into an APL cohort, not a lapse — a policy does not lapse while the cash value can carry the premium [S1] [S10]. Off in the base run. Two of the six carriers do not offer the APL at all [S6] [S13], so the off position is a product variant and not merely a switch.

  • Reinstatement (復活) is not modelled std, and it costs more here than on the chassis. Within three years of lapse a Japanese policy comes back [S1] [S10]; on this product two carriers additionally pay a 学資金 whose payment date fell while the policy was lapsed, provided the policy is later reinstated [S1] [S10]. So lapse is not terminal even for benefits already due, and treating every exit as terminal understates later-duration in force, premium income, staged benefits and the maturity benefit together.

  • Dynamic surrender on the value-to-premium ratio std (optional module, off in base). The chassis’s form carries over, w_dyn(t) = w(t) × min(3.0, max(1.0, 1 + β × max(0, CV(t) / cumprem(t) − 1))) with β = 2.0 std and cumprem(t) = P × min(t, m). On the anchor cell the ratio never reaches 1 — it peaks at 92.0% at maturity — so the module is inert there, which is itself the finding: a 30-year 養老保険 at a 1.00% 予定利率 gives its owner no point at which surrendering beats persisting on value grounds alone.

  • Election of the staged schedule. The type, once elected, cannot be changed after issue [S7], so schedule_id is a model-point attribute and never a projected decision.

  • 免責 and 告知義務違反 incidence are zero in the base run std. Where a claim is refused the composite pays the 保険料積立金 rather than nothing [S2] [S8] — but two carriers on the 学資 cell pay nothing at all, not even the reserve, where the 契約者 intentionally kills the insured child [S1] [S10]. A model that assumes the zero-payment position universally overstates the insurer by the whole reserve.

  • The grace-period trap is not modelled std, and it is the reason the waiver is not an overlay. Stated identically at three carriers: if the waiver event happens while a premium is unpaid inside the grace period, that premium must be paid by the end of the grace period or the waiver is refused [S1] [S6] [S10]. A 契約者 who dies one week into arrears loses the entire benefit. That is a direct interaction between the premium-default decrement and the waiver decrement, and it is why the waiver cannot be applied as an independent multiplier on a premium stream. The annual grid has no arrears state, so the interaction is out of scope and named rather than approximated.

Worked example#

Every figure below was recomputed numerically before it was written.

Anchor cell (point_id = 1) — 養老保険#

Male, 契約年齢 30 (満年齢), 基準保険金額 ¥5,000,000, 保険期間 30 years (満期 at attained age 60), 保険料払込期間 30 years, annual premium ¥181,140 (= 12 × the published ¥15,095 monthly premium for exactly this cell [S9]). T = n = 30 policy years, attained ages 30 to 59. 死亡保険金 = 満期保険金 = ¥5,000,000 R10 [S2] [S8]. No waiver, no loan, no APL, no dividend.

Assumption values used, in full. i_cv = 1.00% [S9]; α = 0.25 of one annual premium, so SC(0) = ¥45,285 std; mort_be_factor = 1.00 std; lapse_rate = 4% / 3% / 2% … 2% / 0% at t = 30 std; E0 = ¥50,000, c0 = 0.90, c_r = 0.03, e(t) = ¥8,000 × 1.01^(t−1), ec = ¥20,000, all std; i_L = 2.40% [S9], unused because loan_pp ≡ 0.

The mortality rates. These are 生保標準生命表2018（死亡保険用）男 rates read at the anchor ages q30 = 0.00068, q31 = 0.00069, q32 = 0.00070, q33 = 0.00072, q34 = 0.00074, q35 = 0.00077, q40 = 0.00118, q45 = 0.00177, q50 = 0.00285, q55 = 0.00422 and q60 = 0.00653 R1 REG-R18, with the intervening ages filled by std log-linear interpolation in ln q rounded to five decimals. They are not illustrative placeholders: every rate here is either read from the published table or interpolated between two rates that were, and mort_table.csv says which each row is.

age

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

q

.00068

.00069

.00070

.00072

.00074

.00077

.00084

.00091

.00099

.00108

.00118

.00128

.00139

.00151

.00163

age

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

q

.00177

.00195

.00214

.00236

.00259

.00285

.00308

.00333

.00361

.00390

.00422

.00461

.00503

.00548

.00598

The cash-value construction. A(30, 30) = 0.74664983 and ä(30, 30) = 25.58836739 on i_cv = 1.00% and the male table, so π = ¥145,896.34 — an implied loading of ¥35,243.66, 19.457% of the gross premium. The resulting values, with SC(t) = 0.25 × 181,140 × (30 − t) / 30:

t

W(t)

SC(t)

CV(t)

cumulative premiums

CV(t) / cum. prem.

1

144,053.26

43,775.50

100,277.76

181,140

55.4%

5

735,250.45

37,737.50

697,512.95

905,700

77.0%

15

2,313,975.49

22,642.50

2,291,332.99

2,717,100

84.3%

29

4,804,598.71

1,509.50

4,803,089.21

5,253,060

91.4%

30

5,000,000.00

0.00

5,000,000.00

5,434,200

92.0%

W(30) = S exactly, which is the identity check_pol_val_terminal() asserts, and the last column never reaches 100% — this contract does not return its premiums even at maturity.

First periods of the base run. Per policy issued, income-positive, to two decimal places. The expenses column carries maintenance, and at t = 1 the acquisition expense as well; the claim handling expense is the separate claim_expenses column beside it. pols_if is the total in force, which on this cell equals pols_if_pay because there is no waiver and therefore no second state.

t

age

q(t)

pols_if(t)

premiums

claims_death

claims_maturity

claims_lapse

expenses

claim_expenses

commissions

net_cf

1

30

0.00068

1.000000

181,140.00

3,400.00

0.00

4,008.38

58,000.00

13.60

163,026.00

−47,307.98

2

31

0.00069

0.959347

173,776.15

3,309.75

0.00

7,113.43

7,751.53

13.24

5,213.28

150,374.92

3

32

0.00070

0.929925

168,446.56

3,254.74

0.00

7,357.98

7,588.93

13.02

5,053.40

145,178.50

4

33

0.00072

0.910688

164,962.07

3,278.48

0.00

9,936.68

7,506.26

13.11

4,948.86

139,278.67

5

34

0.00074

0.891832

161,546.43

3,299.78

0.00

12,432.08

7,424.35

13.20

4,846.39

133,530.63

…

29

58

0.00548

0.520387

94,262.89

14,258.60

0.00

49,715.35

5,500.66

57.03

2,827.89

21,903.35

30

59

0.00598

0.507184

91,871.40

15,164.82

2,520,757.67

0.00

5,414.72

60.66

2,756.14

−2,452,282.61

Trace, year 1. D(1) = 1.000000 × 0.00068 = 0.00068; death claims = 5,000,000 × 0.00068 = 3,400.00; claim expense = 20,000 × 0.00068 = 13.60. Survivors of mortality R(1) = 1 − 0.00068 = 0.999320, so Sr(1) = 0.999320 × 0.04 = 0.0399728; CV(1) = W(1) − SC(1) = 144,053.259234 − 43,775.50 = 100,277.759234, so surrender benefits = 100,277.759234 × 0.0399728 = 4,008.38. Expenses = 50,000.00 + 8,000.00 = 58,000.00, with the claim expense 13.60 beside them; commission = 0.90 × 181,140 = 163,026.00. CF(1) = 181,140.00 − 3,400.00 − 13.60 − 4,008.38 − 50,000.00 − 8,000.00 − 163,026.00 = −47,307.98. Update: l_p(2) = 0.999320 × 0.96 = 0.9593472.

Trace, year 2. Premiums = 181,140 × 0.9593472 = 173,776.15. D(2) = 0.9593472 × 0.00069 = 0.00066195; claims = 5,000,000 × 0.00066195 = 3,309.75; claim expense = 13.24. R(2) = 0.9593472 × 0.99931 = 0.958685250, so Sr(2) = 0.958685250 × 0.03 = 0.028760558; CV(2) = 289,598.918098 − 42,266.00 = 247,332.918098, so surrender benefits = 247,332.918098 × 0.028760558 = 7,113.43. Maintenance = 8,000 × 1.01 × 0.9593472 = 7,751.53; renewal commission = 0.03 × 181,140 × 0.9593472 = 5,213.28. CF(2) = 173,776.15 − 3,309.75 − 13.24 − 7,113.43 − 7,751.53 − 5,213.28 = 150,374.92. Update: l_p(3) = 0.958685250 × 0.97 = 0.929924693.

Trace, year 3. Premiums = 181,140 × 0.929924693 = 168,446.56. D(3) = 0.929924693 × 0.00070 = 0.000650947; claims = 3,254.74; claim expense = 13.02. R(3) = 0.929924693 × 0.99930 = 0.929273746, Sr(3) = 0.929273746 × 0.02 = 0.018585475; CV(3) = 436,655.869405 − 40,756.50 = 395,899.369405, so surrender benefits = 395,899.369405 × 0.018585475 = 7,357.98. Maintenance = 8,000 × 1.01² × 0.929924693 = 7,588.93; renewal commission = 5,434.20 × 0.929924693 = 5,053.40. CF(3) = 168,446.56 − 3,254.74 − 13.02 − 7,357.98 − 7,588.93 − 5,053.40 = 145,178.50.

Trace, the maturity year t = 30. l(30) = 0.507184498, q(30) = 0.00598, so D(30) = 0.003032963 and death claims = 5,000,000 × 0.003032963 = 15,164.82, with claim expense 60.66. R(30) = 0.507184498 × (1 − 0.00598) = 0.504151534, and because lapse_rate(30) = 0 every one of those survivors matures: claims_maturity = 5,000,000 × 0.504151534 = 2,520,757.67. Maintenance = 8,000 × 1.01²⁹ × 0.507184498 = 5,414.72; renewal commission = 5,434.20 × 0.507184498 = 2,756.14. CF(30) = 91,871.40 − 15,164.82 − 60.66 − 2,520,757.67 − 5,414.72 − 2,756.14 = −2,452,282.61, against +21,903.35 one year earlier. The maturity payment is the largest single item in the stream and it is one year wide, and unlike the chassis’s cliff it is a certain payment rather than a behavioural one — the only uncertainty in it is how many policies reach it.

Roll-forward check. Over the 30 years, Σ D(t) = 0.043174852, Σ Sr(t) = 0.452673614 and the maturing survivors R(30) = 0.504151534, summing to 1.000000000, with l(31) = 0.504151534 before the maturity payment and 0 after it. Undiscounted totals per policy issued: premiums 3,931,162.67; death claims 215,874.26; maturity 2,520,757.67; surrender benefits 887,154.17; expenses 247,991.55 (maintenance 197,991.55, acquisition 50,000.00); claim expense 863.50; commission 275,526.68; Σ CF(t) = −217,005.15. Undiscounted, the contract loses money; discounting is out of scope and is what makes the sign meaningful. Half the block reaches maturity — 0.5042 of policies issued — which is the structural difference from every protection product in this library.

henreiritsu() returns 92.0099% = 5,000,000 / 5,434,200, reproducing the derived figure in product-spec.md [S9].

Second cell (point_id = 2) — 学資保険#

契約者 male 契約年齢 30, 被保険者 (the child) 契約年齢 0, 22歳満期 (n = 22), 保険料払込期間 17 years, 基準保険金額 ¥1,000,000, S型 grid at child 契約年齢 0–1, annual premium ¥108,564 (= 12 × ¥9,047 [S11]), waiver = true. Staged benefits at t = 3 / 6 / 12 / 15 / 18 / 20 of 5% / 5% / 10% / 10% / 70% / 10% of S, then 満期保険金 100% at t = 22 [S10] [S11].

Additional assumption values. i_cv = 1.00% [S9]; α = 0.25, so SC(0) = ¥27,141 std; wv_frac = 1.00, wv_load = 1.00, wv_lapse_mult = 1.00, all std; child mortality at attained age t − 1 and 契約者 mortality at attained age 29 + t for t ≤ 17, both from 生保標準生命表2018（死亡保険用）男 R1 REG-R18 on the same std interpolation:

child age

0

1

2

3

4

5–10

11

12

13

14

15

16

17

18

19

20

21

q

.00081

.00056

.00035

.00022

.00015

.00010

.00012

.00014

.00016

.00019

.00023

.00030

.00038

.00046

.00052

.00059

.00062

The rates read from the published table over this range are those at ages 0, 1, 3, 5, 10, 15, 17, 18, 20 and 22 R1 REG-R18; ages 2, 4, 6–9, 11–14, 16, 19 and 21 are the std log-linear fill between them, and mort_table.csv says which each row is. The same split holds over the adult range, where the read ages are 25, 30–35, 40, 45, 50, 55 and 60. The 契約者 rates over ages 30–46 are the anchor cell’s first seventeen. π_g = ¥110,458.94 against a gross premium of ¥108,564 — the −1.745% loading discussed in class (b).

pols_if here is the total in force and pols_if_pay + pols_wv reproduces it row by row; the premium is carried on pols_if_pay alone and every benefit on pols_if.

t

child age

契約者 age

pols_if

pols_if_pay

pols_wv

premiums

claims_death

claims_staged

claims_lapse

expenses

claim_expenses

commissions

net_cf

1

0

30

1.000000

1.000000

0.000000

108,564.00

90.44

0.00

3,441.59

58,000.00

16.20

97,707.60

−50,691.83

2

1

31

0.959222

0.958570

0.000652

104,066.21

120.57

0.00

5,766.83

7,750.52

10.74

3,121.99

87,295.56

3

2

32

0.929925

0.928651

0.001274

100,818.08

110.14

46,479.96

4,946.12

7,588.93

6.51

3,024.54

38,661.89

…

17

16

46

0.699318

0.687606

0.011712

74,649.23

364.78

0.00

24,311.57

6,560.04

4.20

2,239.48

41,169.16

18

17

—

0.685126

0.672338

0.012788

0.00

457.38

479,405.94

14,475.47

6,491.18

5.21

0.00

−500,835.19

20

19

—

0.657442

0.645171

0.012271

0.00

368.92

65,710.05

12,867.48

6,354.10

6.84

0.00

−85,307.38

22

21

—

0.630707

0.618935

0.011772

0.00

391.04

0.00

0.00

6,218.23

7.82

0.00

−636,933.05

claims_maturity is 630,315.97 at t = 22 and zero elsewhere; claims_ph_death is 0.00 in every year, because wv_frac = 1.00.

Trace, year 1. Premium = 108,564.00 × 1.000000 = 108,564.00. Child decrement: D(1) = 1.000000 × 0.00081 = 0.00081; DB(1) = max(108,564 − 0, Wb(1) = 111,653.970487) = 111,653.970487, so death claims = 111,653.970487 × 0.00081 = 90.44 and claim expense = 20,000 × 0.00081 = 16.20. 契約者 decrement: Dp(1) = 1.000000 × (1 − 0.00081) × 0.00068 = 0.000679449, all of it into the waived state. Paying state after mortality = 1 × 0.99919 × 0.99932 = 0.998510551; waived = 0.000679449; R(1) = 0.999190000. g(1) = 0, so no staged benefit. Sr(1) = 0.999190 × 0.04 = 0.039967600; CV(1) = 111,653.970487 − 25,544.4706 = 86,109.499898, so surrender benefits = 86,109.499898 × 0.039967600 = 3,441.59. Expenses = 50,000.00 + 8,000.00 = 58,000.00, with the claim expense 16.20 beside them; commission = 0.90 × 108,564 = 97,707.60. CF(1) = 108,564.00 − 90.44 − 16.20 − 3,441.59 − 58,000.00 − 97,707.60 = −50,691.83. Update: l_p(2) = 0.998510551 × 0.96 = 0.958570129, h(2) = 0.000679449 × 0.96 = 0.000652271.

Trace, year 3 — the first staged benefit. Premium = 108,564 × 0.928651118 = 100,818.08. D(3) = (0.928651118 + 0.001273560) × 0.00035 = 0.000325474; DB(3) = max(3 × 108,564 − 0, Wb(3) = 338,386.301776) = 338,386.30 — the value limb binds and the cumulative-premium limb 325,692.00 does not — so death claims = 338,386.301776 × 0.000325474 = 110.14 and claim expense 6.51. Dp(3) = 0.928651118 × (1 − 0.00035) × 0.00070 = 0.000649828, into the waived state; R(3) = 0.927676262 + 0.001922943 = 0.929599205. Staged benefit: g(3) = 0.05, so claims_staged = 1,000,000 × 0.05 × 0.929599205 = 46,479.96 — paid to the waived state as well as to the paying one. CV(3) = W(3) − SC(3) = 288,386.301776 − 22,351.4118 = 266,034.890011; note that W(3) is the value after the ¥50,000 payment, so the surrender value falls by exactly the benefit. Sr(3) = 0.929599205 × 0.02 = 0.018591984, giving surrender benefits 4,946.12. Maintenance = 8,000 × 1.01² × 0.929924678 = 7,588.93; renewal commission = 0.03 × 108,564 × 0.928651118 = 3,024.54. CF(3) = 100,818.08 − 110.14 − 6.51 − 46,479.96 − 4,946.12 − 7,588.93 − 3,024.54 = 38,661.89.

Trace, year 18 — the 70% payment, and the year the 契約者 stops mattering. No premium (t > m = 17) and therefore no renewal commission. q_p(18) = 0, so the 契約者 decrement is gone and pols_wv now runs off on child mortality and surrender alone: 0.012788161 at the start of year 18 against 0.011712229 at the start of year 17, having stopped growing. D(18) = 0.685125982 × 0.00038 = 0.000260348; DB(18) = max(1,845,588 − 300,000, Wb(18) = 1,756,811.077206) = 1,756,811.08, so death claims = 457.38 and claim expense 5.21. R(18) = 0.684865634; claims_staged = 1,000,000 × 0.70 × 0.684865634 = 479,405.94. CV(18) = W(18) = 1,056,811.077206, down from 1,738,755.93 at t = 17 — the surrender value falls by the ¥700,000 paid, exactly as the sourced constraint requires [S7] — so surrender benefits = 1,056,811.077206 × 0.013697313 = 14,475.47. CF(18) = −457.38 − 5.21 − 479,405.94 − 14,475.47 − 6,491.18 = −500,835.19.

Roll-forward check. Σ D(t) = 0.005018426, Σ (1 − wv_frac) × Dp(t) = 0, Σ Sr(t) = 0.364665608 and the maturing survivors R(22) = 0.630315966, summing to 1.000000000. Undiscounted totals per policy issued: premiums 1,521,101.61; death claims 4,120.71; staged benefits 785,574.68; maturity 630,315.97; surrender benefits 299,647.45; claims_ph_death 0.00; expenses 203,460.43 (maintenance 153,460.43, acquisition 50,000.00); claim expense 100.37; commission 140,083.73; Σ CF(t) = −542,201.73.

What the waiver is worth on this cell. Ignoring lapse, the cumulative probability of entering the waived state over the 17 premium-paying years is 1.861464%, and the EPV of the waived premiums at 1.00% is ¥11,384.94 against a premium EPV of ¥1,702,626.54 — 0.6687% of the premium stream, or about a tenth of one annual premium. The amount at risk is P × (m − t): ¥1,845,588 at issue, which is 1.85 times the 満期保険金 the contract will pay, running off to zero at t = 17 while the maturity benefit is still five years away. Small probability, large amount, running off on a different schedule from every other cash flow in the model — which is exactly the shape of error that survives a sensibility check on the base case. In the projected stream it shows up only as the 1.7% of year-17 premium income that is missing, and in nothing else at all.

henreiritsu() returns 113.7849% = 2,100,000 / 1,845,588, against the carrier’s published “approx. 113.7%” for exactly this plan [S11].

Valuation and reserve pointers#

This library projects gross liability cash flows. Every valuation layer consumes them and is cited, never reproduced.

  • Standard policy reserve (hyōjun sekinin junbikin, 標準責任準備金). 保険業法第116条 obliges the reserve and delegates the accumulation method and the level of the assumed coefficients for long-term contracts REG-R4. 施行規則第68条 fixes the scope, and a conventional 養老保険 or 学資保険 with a fixed 予定利率 and a real 保険料積立金 is squarely in it R3 REG-R7; 第69条 splits the reserve into 保険料積立金, 未経過保険料, 払戻積立金 and contingency reserve (kiken junbikin, 危険準備金), with net level premium method (heijun jun-hokenryō-shiki, 平準純保険料式) as the floor for anything out of scope R3 REG-R8. 平成8年大蔵省告示第48号 sets the method (平準純保険料式, no Zillmer adjustment), the table (生保標準生命表2018（死亡保険用）for contracts concluded from 1 April 2018) and the standard valuation rate (hyōjun riritsu, 標準利率) machinery, which references the lower of the three-year and ten-year mean 10-year JGB yield and is determined annually R4 REG-R10 REG-R11; the 2021 amendments brought USD- and AUD-denominated contracts into scope from 2022-04-01, which is the currency boundary this yen composite sits inside R5 REG-R12. The current numeric 標準利率 could not be established from any retrieved official document R4 R5, so i_std is std and defaults to i_cv = 1.00%, which makes reserve_pp(t) − V(t) = SC(t) exactly testable. 危険準備金 is prescribed by sub-class and is not modelled R3 REG-R8; 価格変動準備金 under 保険業法第115条 is asset-driven and out of scope entirely REG-R3. reserve_pp produces no cash flow.

  • On this product the reserve is also a contractual amount, which the chassis’s framing does not cover. The 約款 use 積立金 and 責任準備金 interchangeably — one carrier defines 積立金 as the 責任準備金 for the base contract computed by the method the company determines [S2] [S3], and a second identically [S13] — and that quantity floors a benefit: the 学資 cell’s 死亡給付金 [S3] [S13], the refused claim [S2] [S8] and the war-risk reduction [S2] [S8] are all defined against it. A model that treats the reserve as purely a valuation output cannot compute this product’s benefits, which is why pol_val_pre_pp is a cash-flow input and reserve_pp is not.

  • ESR. From 31 March 2026 insurers are supervised on 経済価値ベースのソルベンシー規制, with liabilities at 現在推計 plus MOCE, re-measured at each 基準日 on assumptions re-set then, discounted on a prescribed curve and calibrated in principle to 99.5%; early corrective action triggers below 100%, replacing the old ソルベンシー・マージン比率 200% trigger REG-R15 REG-R17. This projection is the 現在推計 cash-flow engine and nothing more: BEL = Σ_t v(t) × [outgo(t) − income(t)] over the recursion above, with v(t), MOCE and the standard-formula coefficients out of scope — the 柱告示 were not opened and their coefficients are unverified REG-R16. The regime change bites on this product specifically: a 30-year 養老保険 written at a 1.00% 予定利率 [S9] is a long, fixed, guaranteed maturity obligation, and the old basis was ロックイン; under a re-measured basis that guarantee is re-valued on each 基準日’s curve.

  • The 意見書 chain. 保険業法第121条第1項第1号 requires the 保険計理人 appointed under 第120条 to confirm in an 意見書 that the reserve is soundly accumulated REG-R5 REG-R6; the IAJ 実務基準 turns that into the 1号収支分析, a forward income-and-outgo analysis over at least ten future years by product segment under prescribed scenarios, with sufficiency tested over the first five REG-R22.

  • Accounting. IFRS 17 is not mandatory in Japan — IFRS applies as 指定国際会計基準 on a voluntary basis REG-R47. J-GAAP statutory reserving, the ESR economic balance sheet and IFRS 17 are three bases over one set of projected cash flows, and this model keeps the cash flows basis-agnostic, with discounting, margins and tax layered on top.

  • Disclosure, binding on the outputs rather than on the values. The supervisory guideline requires the 解約返戻金 amount or its method to be disclosed and the 自動振替貸付 to be at the policyholder’s election with prompt notice (監督指針 IV-1-10, IV-1-12) REG-R14; the statutory 説明義務 covers the surrender-value profile REG-R39. Both bear on a product whose surrender value is below cumulative premiums at every duration on both cells. The 返戻率 raises the sharper question: no FSA, 消費者庁 or 国民生活センター publication specific to its disclosure was located, so any claim that the disclosure is regulated would be unverified — the published ratios are carrier marketing disclosures, and on a 有配当 design part of the ratio is not guaranteed REG-R38.

  • Tax is not modelled. A lump-sum 満期保険金 is 一時所得 and a staged stream is 雑所得 R6 REG-R46; premiums fall in the 一般生命保険料控除 basket R7 R8 REG-R43. jplib models contractual cash flows, not the policyholder’s tax position.

Key sensitivities and model risks#

In rough order of leverage on this product:

  1. The maturity benefit, and how many policies reach it. 0.5042 of the anchor cell’s policies mature, and the payment is ¥2,520,757.67 against a ¥3,931,162.67 premium stream — 64% of all income leaves in one year. Every lapse assumption is therefore a maturity assumption: the surrender-rate table moves the largest cash flow in the model through the survivorship factor, not through the surrender-benefit column.

  2. The cash-value construction. i_cv is sourced [S9], but α is std and carries the whole ¥887,154.17 surrender-benefit stream on the anchor cell. Unlike the chassis, there is no published surrender-value table for either cell to calibrate against [S1] [S2] [S10], so the calibration is inherited rather than fitted, and the construction is more generous in the early durations than one carrier’s qualitative description [S7]. A user with a real 算出方法書 replaces pol_val_pp and changes nothing else.

  3. The waiver decrement. 1.86% cumulative probability against an amount at risk that starts at 1.85 times the maturity benefit. Omitting it understates the liability by 0.66% of the premium stream — small, but invisible: no claim column changes, only premium income. Holding wv_load at 1.00 additionally excludes the accident-caused 身体障害 trigger that three of six carriers write [S1] [S10] [S16], so the base run is on the low side twice over.

  4. The staged schedule. Total receipts range from 100% to 400% of 基準保険金額 across the six carriers [S1] [S3] [S7] [S10] [S13] — a four-fold spread that is an artefact of how each scales 基準保険金額. A model that treats the grid as anything but data is modelling one carrier.

  5. The −1.745% loading on the second cell. A composite that takes a premium from one carrier and a 予定利率 from another produces a net premium above the gross premium, which no real product carries. It is visible, it is a derived output, and it is why the internal-rate diagnostics are printed beside it.

  6. The 予定利率 / 標準利率 gap. The 予定利率 is sourced at 1.00% [S9]; the numeric 標準利率 could not be established R4 R5. On a guaranteed 30-year maturity obligation the spread between them determines whether the statutory reserve behaves at all, and reserve_pp ≥ V ≥ CV is not an invariant under 逆ざや.

  7. Mortality margin, and its two signs. mort_be_factor = 1.00 puts the base run on a valuation table with a roughly-2σ margin REG-R20. On the anchor cell claims move proportionately; on the second cell the child decrement contributes ¥4,120.71 against ¥1.52m of premium income and moving it changes almost nothing, while the same margin on the 契約者 is the difference between a prudent and a best-estimate waiver cost.

  8. 復活, and the 学資金 that survives a lapse. Not modelled, so in force is understated; and on this product a lapse does not even extinguish a benefit already due, because two carriers pay a 学資金 whose date fell during the lapsed period once the policy is reinstated [S1] [S10].

  9. Common-accident dependence between the two lives. The composite treats them as independent std because no retrieved document gives a dependency. Where the 契約者 is the child’s parent, the joint event is exactly the one that matters and it is unmodelled.

Known modeling pitfalls:

  • The maturity benefit is certain, not a decrement. At t = n the survivors are paid S with probability 1 R10 [S2] [S8]. Modelling maturity as a rate, or letting the projection run past t = n on a terminal age imported from the whole-life chassis, is wrong in both directions.

  • lapse_rate(n) must be zero. A surrender at the end of the final policy year and the maturity payment fall on the same anniversary at the same amount; running both double-counts the terminal payment, and running the surrender instead of the maturity misclassifies 61% of the anchor cell’s undiscounted outgo into the wrong column.

  • The policy value must converge on the maturity benefit. pol_val_pp(n) == sum_assured exactly, on both cells. That identity is what makes an endowment a real test of a savings model, and it is the one thing a whole-life chassis can never check.

  • Two lives, two decrements, one policy. The waiver runs on the 契約者’s mortality at y + t − 1; every benefit runs on the 被保険者’s at x + t − 1 [S1] [S10]. Reading one table at one age for both is the most likely implementation error on the second cell — and on the anchor cell the two ages coincide, so it will not show there.

  • The 契約者 decrement stops at m. Every waiver trigger is conditional on the event falling during 保険料払込期間 [S1] [S10]. Carrying q_p past t = m terminates policies the contract does not terminate, and does so in exactly the years when 86% of the second cell’s receipts fall.

  • The waiver produces no benefit outgo. It removes premium income and leaves every claim column unchanged [S1] [S10] [S13]. Booking a “waiver benefit” double-counts; and because omitting the waiver altogether changes no claim column either, neither error is visible in a benefit reconciliation.

  • Premiums on a waived policy are deemed paid. The return-of-premiums death benefit keeps growing at P × min(t, m) on a policy that pays nothing, and the surrender value is the same in both states for the same reason [S1] [S10] [S13]. Netting the waived premiums out of either understates both.

  • 高度障害 is inside the death rate; accident-caused 身体障害 is not. 生保標準生命表2018（死亡保険用）already includes 高度障害 REG-R20 R2, so a separate disability decrement on the 被保険者 double-counts — but the waiver’s third trigger, 身体障害 from a listed accident within 180 days [S1] [S10] [S16], is genuinely additional and wv_load = 1.00 leaves it out. The two cases point opposite ways.

  • A waiver carve-out terminates the contract; it does not merely remove the waiver. Three-year suicide of the 契約者, the 後継保険契約者’s intentional act and war each end the policy against the 責任準備金 paid to the 契約者’s heirs [S1] [S7] [S10]. claims_ph_death is zero in the base run and must become non-zero as soon as wv_frac < 1.

  • The staged benefit is not a claim and not a decrement. It is paid on survival at a fixed date to a policy still in force, in both states, and it terminates nothing [S10] [S11]. Weighting it by a decrement rate, or paying it only from the premium-paying state, understates it.

  • Each staged benefit reduces the surrender value by its own amount. CV falls from 1,738,755.93 to 1,056,811.08 across t = 17 → 18 on the second cell, and one carrier computes the value from the elapsed months and the 学資金 timing [S1] [S7]. A model that pays the staged benefit beside the value rather than out of it inflates every later surrender.

  • The staged schedule is data. It is read from a table keyed by schedule_id, and the J variant — one payment of 100%, then maturity — must run without touching the code [S10].

  • Both limbs of the 学資 death benefit must be evaluated. On the composite’s std basis the reserve limb dominates at every duration, so the max never switches; that is a property of this cell’s negative loading, not of the contract [S3] [S13], and a point with a positive loading binds the other way. Hard-coding either limb passes on this cell and fails on the next.

  • henreiritsu() is a contractual ratio, not a model output ratio. It reads P × m and the scheduled benefits, never the projected premium income or the probability-weighted claims; it is undefined for a policy that surrenders and unbounded for one that is waived; and computed from a 月払 premium on an annual grid it sits below the carrier’s own published figure [S11] [S16].

  • There is no cliff on this product. No retrieved document offers a 低解約返戻金型 form of either cell. Importing the chassis’s k = 0.70 multiplier, its step at m, or its 15% surrender spike models a product that does not exist here.