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.

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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).

• Time index — three of them, and they are not the same. The projection index t is 0-based and counts policy months: t = 0 is the first policy month and t = 12n − 1 the last, proj_len is the number of projected months so the frame is t = 0 … proj_len − 1, and the contractual policy year is the 1-based label y(t) = 1 + ⌊t/12⌋ with duration(t) = ⌊t/12⌋ beside it. Month t runs from time t to time t + 1; flows at the start of the month fall at t and flows at its end at t + 1. Beside it runs the anniversary index k, in years, with k = 0 at issue: everything that is a value at a point in time rather than a flow during a period is indexed by k — W(k), Wb(k), SC(k), V(k), CV(k), g(k), G(k), EPV(k), the loan balance L(k) and cumulative premiums P × min(k, m) — and none of those numbers moved when the projection index became a month. SC(0) is the deduction at issue and W(n) = S the value at maturity, as before. A benefit falling between two anniversaries reads the value at the elapsed month u instead, by linear interpolation std — from the value after the staged benefit at one anniversary to the value before the one at the next, which is the curve the contract traces. The 算出方法書 that would state the real within-year rule is a 基礎書類 filed with the 金融庁 and is not published REG-R2.

• Projection frequency. Monthly, on policy months (Endowment_JP_S). The contract is quoted in years — the term, the 保険料払込期間, the staged grid and the lapse curve are all annual — so the monthly step is finer than the guarantees rather than finer than the product. Three things follow. The 年払 premium falls in one month out of twelve instead of being smeared across a year. Every payment that is a payment on a date — each 学資金, the 満期保険金 — falls in the single month whose end is that date, so the maturity payment is one month wide rather than one year. And the final-period surrender carve-out shrinks from a policy year to a month, which moves the maturing fraction. 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 model still 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. The monthly grid does not fix that, because the model point table carries no calendar date to fix it with; what it does is make the approximation visible, since a staged payment now occupies one month and the months it might have occupied instead are rows a reader can point at.

• Timing conventions std. Premium at the start of the anniversary months t = 0, 12, …, 12(m − 1), in advance, and zero in the eleven months between each pair; maintenance expense at the start of each month, a twelfth of the annual amount, inflating once a policy year; renewal commission with the premium it is a percentage of; acquisition expense and initial commission at issue (the start of month t = 0); death claims and claim expenses at the end of the month of death; the 学資金 and the 満期保険金 at the end of the single month whose closing instant is the anniversary they fall on, to policies surviving that month’s mortality; surrenders at the end of the month, after deaths and after any staged benefit just paid, valued on the surrender value net of it.

• Rate conversion std. Both mortality decrements — the 被保険者’s and the 契約者’s — and voluntary surrender are quoted per annum and applied per month on the effective convention r_m = 1 − (1 − r)^(1/12), so twelve months compound back to the annual rate exactly. The premium-default proportion that feeds the APL is not converted: it is the failure to pay one premium on one date, and is applied once per premium.

• 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 month t is therefore x + ⌊t/12⌋ exactly, stepping on the anniversary. On the 学資 cell there is a second age, the 契約者’s y + ⌊t/12⌋, which runs an entirely separate decrement over the months t = 0 … 12m − 1 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: 12n months, t = 0 … 12n − 1. Every state closes at the end of the last one, l(12n) = 0, and the closing cash flow is a certain payment of S to the survivors at anniversary n, which is the close of the final month — 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.

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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 composite’s premium is a 月払 one, so the model’s derived 返戻率 is a monthly-basis ratio and sits below a true 年払 figure. The monthly projection grid does not change that: the grid is when the model looks, the payment frequency is what the 契約者 chose, and the two are independent.

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

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State variables

Variable	Description	Updated
The first block runs on the monthly index t; the second on the anniversary index
k, in years; the third reads the second at an elapsed month u.

Variable	Description	Updated
pols_if(t)	Total in-force probability at the start of month t, pols_if = pols_if_pay + pols_wv; pols_if(0) = 1	sum of the two states
pols_if_pay(t)	In-force probability in the premium-paying state at the start of month t; pols_if_pay(0) = 1	monthly recursion
pols_wv(t)	In-force probability in the waived state at the start of month t; pols_wv(0) = 0; identically 0 on the 養老 cell	monthly recursion
mort_rate(t)	被保険者 annual mortality (incl. 高度障害) applying in month t	table lookup at x + ⌊t/12⌋
mort_rate_mth(t)	The same rate per month, 1 − (1 − q)^(1/12)	conversion std
mort_rate_ph(t)	契約者 annual mortality driving the waiver, t < 12m only; 0 on the 養老 cell	table lookup at y + ⌊t/12⌋
mort_rate_ph_mth(t)	The same rate per month	conversion std
lapse_rate(t)	Annual voluntary surrender rate applying in month t	assumption table, at policy year 1 + ⌊t/12⌋
lapse_rate_mth(t)	The same rate per month	conversion std
default_rate(t)	Premium-default proportion feeding the APL module (0 in base); not converted, and zero outside anniversary months	assumption table, at policy year 1 + ⌊t/12⌋

Variable	Description	Updated
benefit_pct(k)	g(k) — the staged benefit due at anniversary k, as a fraction of S	schedule table
prem_cum_pp(k)	P × min(k, m) — cumulative premiums due over the first k policy years	closed form
pol_val_pp(k)	W(k) — policy value at anniversary k, after any staged benefit due at k	closed form
pol_val_pre_pp(k)	Wb(k) = W(k) + S × g(k) — the same value before that benefit	closed form
surr_charge_pp(k)	SC(k) — the acquisition deduction embedded in the surrender value	closed form
cv_pp(k)	CV(k) — payable 解約返戻金 at anniversary k	closed form
reserve_pp(k)	平準純保険料式 policy reserve, reference quantity only — never a cash flow	closed form
loan_pp(k)	Outstanding APL + 契約者貸付 principal and interest at anniversary k	annual recursion

Variable	Description	Updated
prem_cum_pp_m(u)	P × min(⌈u/12⌉, m) — premiums actually due by elapsed month u	step function
pol_val_pre_at_m(u)	Wb(u) — policy value at elapsed month u, before any staged benefit due at u	interpolation std
pol_val_at_m(u)	W(u) — the same value after it	Wb(u) − S × g(u/12) at anniversaries
surr_charge_at_m(u)	SC(u) — the deduction at elapsed month u	the same linear schedule, read finely
cv_at_m(u)	CV(u) — payable 解約返戻金 at elapsed month u	max(W(u) − SC(u), 0)

The anniversary family is read at k = ⌊t/12⌋ + 1 by the flows of the anniversary months — the closing value of the policy year — and result_val() therefore publishes one row per anniversary k, not one per projection row. The *_at_m family is read at u = t + 1, the closing instant of month t, by every flow in between; at u = 12k the two agree by construction, which check_staged_value asserts.

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 suppression multiplier (the chassis calls it k; k here is the anniversary index in years and nothing else). 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.

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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 anniversary 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(k)	5% / 5% / 10% / 10% / 70% / 10% of S at anniversaries k = 3 / 6 / 12 / 15 / 18 / 20	[S10] [S11]; grid std, timing std
満期保険金 — 学資 cell	S at anniversary k = 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 − k) / 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(k) = α × P × max(0, m − k) / m,     α = 0.25

On the anchor cell that is SC(0) = ¥45,285 at issue, 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 anniversary k = n on the 養老 cell; on the 学資 cell the ratio saw-tooths with the schedule, peaking at 98.4% at k = 11 — the anniversary before the third 学資金 — and standing at 94.2% at k = 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 ¥3,988.78 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 (1 + ⌊t/12⌋)	1	2	3 … n−1	n
Months t	0 … 11	12 … 23	24 … 12n−13	12n−12 … 12n−1
lapse_rate(t) std, per annum	4%	3%	2%	2%, then 0 in the last month

The rates in the table are annual and the model applies them per month on the effective convention w_m = 1 − (1 − w)^(1/12) std, so twelve months of surrender compound back to the annual rate exactly and the in-force ladder at the anniversaries is the one the annual grid produced. On the waived state the same table applies, multiplied by wv_lapse_mult = 1.00 std, and the multiplier acts on the monthly rate rather than the annual one. Both rates are keyed in lapse_table.csv by the contractual policy year, a 1-based label the projection reaches as 1 + ⌊t/12⌋; the file’s policy_year column is not the frame’s t and its values did not move when the frame became monthly. 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 払込満了 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, the rate is forced to 0 std in the final month t = 12n − 1: a surrender at the close of that month and the maturity payment fall at the same instant at the same amount, and an owner one month from a guaranteed S does not take CV(n) = S early. The carve-out is one month and not the final policy year — the eleven months before it carry the ordinary 2%, which is why the maturing fraction moved when the grid did. 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, policy years 2 … m — the anniversary months t = 12, 24, …, 12(m − 1) — on the premium-paying state only std
Maintenance expense e(t)	¥8,000 p.a., charged as ¥8,000 / 12 a month over t = 0 … 12n − 1, inflating at 1.0% p.a. as 1.01^⌊t/12⌋ so the step falls once a policy year, 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	month index, 0-based: t = 0 … 12n − 1; policy year y(t) = 1 + ⌊t/12⌋; the 被保険者’s attained age in month t is x + ⌊t/12⌋
k	anniversary index in years, k = 0 at issue: month t closes policy year k = ⌊t/12⌋ + 1 when (t + 1) mod 12 = 0
u	elapsed month at which a value is read, u = t + 1 for the flows of month t; u = 12k is anniversary k
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 the anniversary months t = 0, 12, …, 12(m − 1)
g(k)	staged 学資金 due at anniversary k, as a fraction of S; 0 on the 養老 cell
G(k)	Σ_{s ≤ k} g(s) — cumulative staged fraction paid to and including anniversary k
q(t), q_p(t)	被保険者 annual mortality applying in month t; 契約者 annual mortality, zero from t = 12m on
q_m(t), q_pm(t)	the same two per month, 1 − (1 − q)^(1/12) std
w(t), w_m(t)	annual voluntary surrender rate applying in month t, and the same per month
u(t)	premium-default proportion (APL module): one decision on one date, never converted, zero outside anniversary months
l(t)	total in-force probability at the start of month 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 month t; expected 契約者 decrements in month t
R(t)	expected in force at the end of month t, after mortality, before surrender
Sr(t)	expected surrenders at the end of month t
A(z, j), ä(z, j)	j-year endowment-assurance EPV of 1 at age z; j-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(k), Wb(k)	policy value at anniversary k, after and before the staged benefit due at k
SC(k), V(k), CV(k)	acquisition deduction; ordinary surrender value; payable 解約返戻金, all at anniversary k
W(u), Wb(u), SC(u), CV(u)	the same four read at an elapsed month u, by linear interpolation std
DB(t)	death benefit for a death in month t, payable at the end of it
L(k)	loan + APL principal and interest at anniversary k — it compounds annually, on the 契約応当日
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 month 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 month — e(t) is a twelfth of the annual maintenance expense, and P falls in one month out of twelve rather than being spread over the year. g(k) 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(k) is read from benefit_schedule_table.csv, keyed by schedule_id, one row per payment, with a provenance column on every row. The key column is k, the anniversary the payment falls on with k = 0 at issue — a time point in years, already 0-based, and not the projection’s month index: the payment at k is the staged claim of the single month t = 12k − 1, whose closing instant is that anniversary.

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

where A(z, j) is the j-year endowment assurance — 1 at the end of the year of death within j years, or 1 on survival to j. At k = n, A(x + n, 0) = 1 and ä(·, 0) = 0, so W(n) = S exactly, by construction; at k = 0, π is defined so that W(0) = 0. 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(k) = S × [ Σ_{s > k} g(s) · v^(s−k) · (s−k)p_(x+k)  +  v^(n−k) · (n−k)p_(x+k) ]
π_g    = EPV(0) / ä(x, m)
W(k)   = EPV(k) − π_g × ä(x + k, max(m − k, 0))
Wb(k)  = W(k) + S × g(k)
DB(t)  = max( P × min(t + 1, m) − S × G(t) − L(t),  Wb(t + 1) )

The Σ_{s > k} is what makes W(k) the value after the staged benefit due at k, 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 k = n there is no future staged benefit and no future premium, so W(n) = S exactly here too.

DB(t) is the only place all three indices meet in one line, and each term sits on the clock it belongs to. A death in month t is paid at the end of it, so the value limb is the interpolated Wb(t + 1) at elapsed month u = t + 1; the premiums due are the min(⌈(t + 1)/12⌉, m) that have actually fallen by then, which steps up once a policy year rather than once a period; and the staged benefits already received are those at anniversaries up to and including ⌊t/12⌋, which is G(⌊t/12⌋), because a payment falling at the close of month t is still inside Wb(t + 1).

Then, on both cells, at every anniversary k,

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

with no 低解約返戻金型 multiplier: CV and V are the same series on this product. Between anniversaries the three are read at an elapsed month u by linear interpolation std — Wb(u) from W(k) to Wb(k + 1), which is the curve the contract traces between one staged benefit and the next, and SC(u) = α P (12m − u) / 12m, which is the same linear run-off read finely rather than a second schedule — with CV(u) = max(0, W(u) − SC(u)) as before. The 算出方法書 that would state the carrier’s real within-year rule is a 基礎書類 filed with the 金融庁 and is not published REG-R2, so the interpolation is a standardization and is flagged as one; at u = 12k it reproduces the anniversary value exactly, which check_staged_value asserts.

The premium term in DB(t) is deemed-paid, not cash-paid. P × min(⌈(t + 1)/12⌉, m) counts every premium falling due by the end of month 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(k) 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(k) 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 = 0 … 12n − 1, every line on the monthly rates:

q_pm(t)       = 0  for t ≥ 12m                        (no premium left to waive)
l(t)          = l_p(t) + h(t)                         (total in force)
D(t)          = l(t) × q_m(t)                          (被保険者 deaths, both states)
Dp(t)         = l_p(t) × (1 − q_m(t)) × q_pm(t)         (契約者 decrements, paying only)
to waived     = wv_frac × Dp(t)
terminating   = (1 − wv_frac) × Dp(t)                 (pays Wb(t + 1) to the heirs)

l_p_after(t)  = l_p(t) × (1 − q_m(t)) × (1 − q_pm(t))
h_after(t)    = h(t) × (1 − q_m(t)) + wv_frac × Dp(t)
R(t)          = l_p_after(t) + h_after(t)

l_p(t + 1)    = l_p_after(t) × (1 − w_m(t))
h(t + 1)      = h_after(t) × (1 − min(1, wv_lapse_mult × w_m(t)))

The waiver multiplier acts on the monthly surrender rate, not on the annual one: a waived policy that surrenders at half the ordinary pace does so at half the pace in every month, rather than at half an annual rate spread unevenly over twelve. Twelve months of each line compound back to the annual recursion the previous grid ran, so the transition probabilities at the anniversaries are the ones it produced.

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_pm(t) = 0 for t ≥ 12m is a modelling ruling and earns its own sentence. The premium-paying months are t = 0 … 12m − 1, so the decrement stops with the last of them. 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 the months t = 204 … 263, policy years 18 to 22 of the 22-year term — the years in which 86% of the receipts fall — and carrying the decrement through them would move a further 0.8250% of policies out of the premium-paying state, which wherever wv_frac < 1 terminates a share of them and deletes their maturity benefits.

Processing order (month t = 0 … 12n − 1, i.e. policy years 1 … n)

1. Start of the month — premium, in anniversary months only. Collect P × l_p(t) when t mod 12 = 0 and t < 12m — on the paying state alone, never on l(t) — and nothing in the other eleven months. 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 the month — expenses and commission. e(t) × l(t) every month, a twelfth of the annual amount, on the whole in force; renewal commission c_r × P × l_p(t) in the anniversary months t = 12, 24, …, 12(m − 1), on the paying state only, because it follows the premium it is a percentage of. At t = 0 additionally E0 and c0 × P.

3. Start of the month — APL test (module on), in anniversary months only: the premium default is a failure to pay one premium on one date. Chassis, unchanged, run against CV.

4. Values. Compute Wb(t + 1), W(t + 1), SC(t + 1), CV(t + 1) at the closing elapsed month u = t + 1, by interpolation std between the anniversaries u lies between; in an anniversary month they are the anniversary values Wb(k), W(k), SC(k), CV(k) with k = (t + 1)/12.

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

6. End of the month — 契約者 decrement, on the paying state only and only for t < 12m: Dp(t) = l_p(t) × (1 − q_m(t)) × q_pm(t), split by wv_frac into a transition to the waived state and a termination paying Wb(t + 1).

7. End of the month — staged benefit, in anniversary months only. S × g(k) × R(t) when t = 12k − 1, to everything in force at that anniversary, in both states. It is not a decrement and it terminates nothing. In the other eleven months it is zero: a 学資金 is a payment on a date.

8. End of the month — maturity, at t = 12n − 1 only. S × R(12n − 1), at anniversary n. The carve-out from surrender is that single month, not the whole final year.

9. End of the month — surrenders, on survivors of both mortality decrements, valued on CV(t + 1) — that is, net of any staged benefit just paid: Sr(t) = l_p_after(t) × w_m(t) + h_after(t) × min(1, wv_lapse_mult × w_m(t)); outgo max(0, CV(t + 1) − L(⌊t/12⌋)) × Sr(t). The waiver multiplier is applied to the monthly rate, so a waived policy surrenders at half the pace every month rather than at half an annual rate spread unevenly.

10. Loan roll-up and in-force update. The loan and APL balances compound annually, at the 契約応当日, because the 約款 states a 年利 capitalised there; the populations l_p(t + 1) and h(t + 1) update every month, as above.

11. At the end of t = 12n − 1 everything closes: l(12n) = l_p(12n) = h(12n) = 0. There are no tail states.

Net cash flow

Income-positive, per policy issued:

CF(t) = P × l_p(t) × 1{t mod 12 = 0, t < 12m}         (premiums)
      − DB(t) × D(t)                                  (被保険者 death claims)
      − ec × D(t)                                     (claim expense)
      − Wb(t + 1) × (1 − wv_frac) × Dp(t)             (契約者 death, waiver refused)
      − S × g((t + 1)/12) × R(t) × 1{(t+1) mod 12 = 0}  (staged 学資金)
      − S × R(12n − 1) × 1{t = 12n − 1}               (満期保険金)
      − max(0, CV(t + 1) − L(⌊t/12⌋)) × Sr(t)         (surrender benefits)
      − e(t) × l(t)                                   (maintenance expense, a twelfth a month)
      − c_r × P × l_p(t) × 1{t mod 12 = 0, 12 <= t < 12m}  (renewal commission)
      − (E0 + c0 × P) × 1{t = 0}                      (acquisition)

net_cf is income-positive throughout, so there is no outgo-positive liability_cf companion on this product: one stream, one sign, one name. 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(12n − 1) = 1,   and   l(12n) = 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 at the final anniversary, 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_k g(k) + 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 is a lower bound on the carrier’s own 年払 figure. The projection now steps in months, but the premium it collects is still the 年払 one: the monthly grid changed when the premium falls, not which premium it is, and ρ did not move.

---

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 + 1) / cumprem(t + 1) − 1))) with β = 2.0 std and cumprem(k) = P × min(k, m), both read at the period’s closing anniversary. 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 model has no arrears state — the monthly grid is now fine enough to carry one, but the grace period is a calendar-day rule the model point table gives no date for — so the interaction is out of scope and named rather than approximated.

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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]). n = 30 policy years, t = 0 … 359 months, 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 at issue std; mort_be_factor = 1.00 std; lapse_rate = 4% / 3% / 2% … 2% per annum, 0% in the final month t = 359 std; E0 = ¥50,000, c0 = 0.90, c_r = 0.03, e(t) = ¥8,000 / 12 × 1.01^⌊t/12⌋ a month, 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(k) = 0.25 × 181,140 × (30 − k) / 30, are indexed by the anniversary k, in years (k = 0 at issue, and k is the close of the month t = 12k − 1); the months in between read them by interpolation std:

k	W(k)	SC(k)	CV(k)	cumulative premiums	CV(k) / 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 months of the base run. Per policy issued, income-positive, to two decimal places, indexed by the 0-based policy month t with the contractual policy year y(t) beside it. The expenses column carries a twelfth of the annual maintenance charge, and at t = 0 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.

Two columns are non-zero in one month out of twelve — the 年払 premium and the renewal commission that follows it — and the maturity payment in exactly one month of the whole 360.

t	y(t)	age	pols_if(t)	premiums	claims_death	claims_maturity	claims_lapse	expenses	claim_exp	commissions	net_cf
0	1	30	1.000000	181,140.00	283.42	0.00	0.00	50,666.67	1.13	163,026.00	−32,837.22
1	1	30	0.996547	0.00	282.44	0.00	0.00	664.36	1.13	0.00	−947.94
2	1	30	0.993107	0.00	281.47	0.00	0.00	662.07	1.13	0.00	−944.67
11	1	30	0.962671	0.00	272.84	0.00	327.82	641.78	1.09	0.00	−1,243.53
12	2	31	0.959347	173,776.15	275.90	0.00	273.66	645.96	1.10	5,213.28	+167,366.24
…
358	30	59	0.496231	0.00	1,239.84	0.00	4,157.88	441.48	4.96	0.00	−5,844.16
359	30	59	0.495148	0.00	1,237.14	2,474,504.99	0.00	440.52	4.95	0.00	−2,476,187.59

Trace, t = 0 (the first policy month). q(0) = 0.00068 is the annual table rate and q_m(0) = 1 − (1 − 0.00068)^(1/12) = 0.0000566843 the decrement applied, so D(0) = 0.0000566843; death claims = 5,000,000 × that = 283.42; claim expense = 1.13. Survivors of mortality R(0) = 0.9999433157, and w_m(0) = 1 − (1 − 0.04)^(1/12) = 0.0033960532, so Sr(0) = 0.0033958607. The surrender benefit is nil, and that is the product rather than a rounding: at the end of the first month the interpolated policy value is W(1) / 12 = 12,004.44 against a 解約控除 of 45,285 × 359/360 = 45,159.21, so CV = max(0, W − SC) = 0. The 約款’s 「ご契約後短期間で解約されたときには、解約返還金がない場合があります」 [S2] is a statement the annual grid could not make: at the first anniversary the value has already outrun the deduction and CV(1) is ¥100,277.76. On this cell the crossover is the fourth month. Expenses = 50,000.00 + 8,000/12 = 50,666.67; commission = 0.90 × 181,140 = 163,026.00. CF(0) = 181,140.00 − 283.42 − 1.13 − 0.00 − 50,666.67 − 163,026.00 = −32,837.22. Update: l_p(1) = 0.9999433157 × 0.9966039468 = 0.996547.

Trace, t = 12 (the first month of policy year 2). The premium falls again — one of the twelve months that carry it — at 181,140 × 0.959347 = 173,776.15, and the renewal commission with it at 0.03 × 173,776.15 = 5,213.28. The attained age steps to 31, so q(12) = 0.00069; the lapse rate steps to 3%. Maintenance = (8,000 / 12) × 1.01 × 0.959347 = 645.96. CF(12) = 173,776.15 − 275.90 − 1.10 − 273.66 − 645.96 − 5,213.28 = +167,366.24.

Trace, the maturity month t = 359. The 満期保険金 falls at the anniversary 30, which is the close of the month 359, so it is one month wide rather than one year. l(359) = 0.495148, q(359) = 0.00598 and q_m = 0.000499704, so D(359) = 0.000247428 and death claims = 1,237.14 with claim expense 4.95. R(359) = 0.494901, and because lapse_rate(359) = 0 every one of those survivors matures: claims_maturity = 5,000,000 × 0.494901 = 2,474,504.99. CF(359) = −1,237.14 − 4.95 − 2,474,504.99 − 440.52 = −2,476,187.59, against −5,844.16 one month earlier.

The maturity payment is the largest single item in the stream and on this grid it is one month wide. Unlike the chassis’s behavioural cliff it is a certain payment — the only uncertainty in it is how many policies reach it.

The surrender carve-out shrank with the grid, and that changed the answer. lapse_rate is zero in the final period so that a surrender and the maturity payment, which fall at the same instant at the same amount, are not both booked. On the annual grid that suppressed surrender for the whole of policy year 30 — twelve months in which an owner could in fact still surrender. Here only the month whose end is the maturity date is suppressed, so the other eleven carry the ordinary 2%, and the maturing fraction falls from 0.5042 to 0.4949 accordingly. That is the largest single difference between the two grids on this cell.

Roll-forward check. Over the 360 months, Σ D(t) = 0.042768495, Σ Sr(t) = 0.462330508 and the maturing survivors 0.494900998, summing to 1.000000000, with l(360) = 0. Undiscounted totals per policy issued: premiums 3,931,162.67; death claims 213,842.47; maturity 2,474,504.99; surrender benefits 899,875.29; expenses 245,871.00 (maintenance 195,871.00, acquisition 50,000.00); claim expense 855.37; commission 275,526.68; Σ CF(t) = −179,313.13. Undiscounted, the contract loses money; discounting is out of scope and is what makes the sign meaningful. Half the block reaches maturity — 0.4949 of policies issued — which is the structural difference from every protection product in this library.

Premium income and commission are identical to the annual grid’s, because both are annual and fall at the same anniversaries on the same survivorship; what moved is the benefit side and the maturity fraction.

henreiritsu() returns 92.0099% = 5,000,000 / 5,434,200, reproducing the derived figure in product-spec.md [S9] — a contractual ratio, unchanged by the projection grid.

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 anniversaries k = 3 / 6 / 12 / 15 / 18 / 20 of 5% / 5% / 10% / 10% / 70% / 10% of S, then 満期保険金 100% at k = 22 [S10] [S11]. Each of those payments is the staged claim of the single month t = 12k − 1 — 35, 71, 143, 179, 215, 239 and 263 — and zero in the other 257.

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/12⌋ and 契約者 mortality at attained age 30 + ⌊t/12⌋ for t < 204, 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. The index is the 0-based policy month, so the staged payment due at anniversary k falls in the single month t = 12k − 1 — months 35, 71, 143, 179, 215 and 239 on this grid.

t	y(t)	child age	契約者 age	pols_if	pols_if_pay	pols_wv	premiums	claims_death	claims_staged	claims_lapse	expenses	claim_exp	commissions	net_cf
0	1	0	30	1.000000	1.000000	0.000000	108,564.00	7.33	0.00	0.00	50,666.67	1.35	97,707.60	−39,818.95
1	1	0	30	0.996537	0.996480	0.000056	0.00	7.31	0.00	0.00	664.36	1.35	0.00	−673.01
2	1	0	30	0.993085	0.992973	0.000113	0.00	7.28	0.00	3.95	662.06	1.34	0.00	−674.63
35	3	2	32	0.912569	0.910734	0.001835	0.00	9.01	45,627.11	408.37	620.61	0.53	0.00	−46,665.63
36	4	3	33	0.911007	0.909123	0.001884	98,698.00	6.42	0.00	422.51	625.74	0.33	2,960.94	+94,682.06
…
192	17	16	46	0.699318	0.687606	0.011712	74,649.23	28.35	0.00	1,905.39	546.67	0.35	2,239.48	+69,928.99
204	18	17	—	0.685126	0.672338	0.012788	0.00	37.76	0.00	2,005.55	540.93	0.43	0.00	−2,584.68
215	18	17	—	0.672321	0.659771	0.012549	0.00	37.41	470,609.46	1,195.15	530.82	0.43	0.00	−472,373.26
239	20	19	—	0.645072	0.633031	0.012041	0.00	30.17	64,504.36	1,062.39	519.54	0.56	0.00	−66,117.02
263	22	21	—	0.618782	0.607233	0.011550	0.00	31.98	0.00	0.00	508.39	0.64	0.00	−619,291.48

claims_maturity is 618,750.47 at t = 263, the last month, and zero elsewhere; claims_ph_death is 0.00 in every month, because wv_frac = 1.00.

Trace, t = 0 (the first policy month) — and the max in DB finally switches. Premium = 108,564.00 × 1.000000 = 108,564.00. Child decrement: the annual rate is q(0) = 0.00081 and the monthly one q_m(0) = 0.0000675251, so D(0) = 0.0000675251. The death benefit is DB(0) = max(cumprem(1) − S·G(0) − L, Wb(1)) read at the end of the month: the return-of-premiums limb is one annual premium, ¥108,564, and the value limb is the interpolated Wb at elapsed month 1, ¥9,304.50 — so the premium limb binds. Death claims = 108,564 × 0.0000675251 = 7.33; claim expense = 1.35.

That is worth stopping on, because the notes’ own instruction is that both limbs must be evaluated and the annual grid never switched between them: at the first anniversary the policy value has already reached ¥111,653.97 against one premium of ¥108,564, so the value limb bound at every duration and a model that hard-coded it would have passed. The monthly grid makes the crossover visible — cumulative premiums step up by a whole 年払 premium in each anniversary month while the value accrues through the year to overtake it, so the refund limb binds early in each policy year and the value limb late in it. It switches 85 times in 264 months: eleven months of policy year 1, then fewer each year — ten, ten, nine, eight … — until the value pulls clear for good in policy year 13. Hard-coding either limb is right eleven months a year at best.

契約者 decrement: q_p(0) = 0.00068 annually and q_p,m(0) = 0.0000566843 a month, so Dp(0) = 0.0000566805, all of it into the waived state. The surrender benefit is nil in the first months for the same reason as on the 養老 cell: the interpolated value has not yet outrun the 解約控除. Expenses = 50,000.00 + 8,000/12 = 50,666.67; commission = 0.90 × 108,564 = 97,707.60. CF(0) = 108,564.00 − 7.33 − 1.35 − 50,666.67 − 97,707.60 = −39,818.95.

Trace, t = 35 — the first staged benefit, and it is one month wide. g(3) = 0.05 falls at the anniversary 3, which is the close of the month 35, so claims_staged = 1,000,000 × 0.05 × R(35) = 45,627.11 — paid to the waived state as well as to the paying one, and nowhere else in the twelve months of policy year 3. The value falls by exactly that benefit at the anniversary, which is the sourced constraint [S7] and is what the interpolation is built to respect: pol_val_pre_at_m(u) runs from the value after the staged payment at one anniversary to the value before the one at the next, so a 祝金 is never smeared backwards over the twelve months preceding it.

Trace, t = 215 — the 70% payment. The 契約者 decrement has been gone since the month 204 (q_p = 0 from 12m = 204), so pols_wv runs off on child mortality and surrender alone. claims_staged = 1,000,000 × 0.70 × R(215) = 470,609.46 in that one month, and the surrender value falls by the ¥700,000 paid at that anniversary: CV(17) = 1,738,755.93 against CV(18) = 1,056,811.08.

Roll-forward check. Σ D(t) = 0.004962269, Σ (1 − wv_frac) × Dp(t) = 0, Σ Sr(t) = 0.376287258 and the maturing survivors 0.618750473, summing to 1.000000000. Undiscounted totals per policy issued: premiums 1,521,101.61; death claims 3,988.78; staged benefits 771,160.39; maturity 618,750.47; surrender benefits 308,128.19; claims_ph_death 0.00; expenses 201,918.51 (maintenance 151,918.51, acquisition 50,000.00); claim expense 99.25; commission 140,083.73; Σ CF(t) = −523,027.70. Premium income and commission are identical to the annual grid’s. The maturing fraction fell, from 0.6303 to 0.6188, for the same reason as on the 養老 cell: the final-period surrender carve-out is now one month rather than twelve, so eleven more months of ordinary surrender run before maturity.

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 − k) at anniversary k: ¥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 anniversary 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 the last premium-paying period’s 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].

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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(k) − V(k) = SC(k) 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.

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Key sensitivities and model risks

In rough order of leverage on this product:

1. The maturity benefit, and how many policies reach it. 0.4949 of the anchor cell’s policies mature, and the payment is ¥2,474,504.99 against a ¥3,931,162.67 premium stream — 63% of all income leaves in one month, t = 359. 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. The monthly grid raised the leverage slightly rather than lowering it: the carve-out that stops the last surrender from colliding with the maturity payment is now one month rather than one policy year, so eleven more months of surrender run before the benefit falls and the maturing fraction is 0.4949 where the annual grid said 0.5042.

2. The cash-value construction, and now also its within-year shape. i_cv is sourced [S9], but α is std and carries the whole ¥899,875.29 surrender-benefit stream on the anchor cell. The monthly grid adds a second standardization on top of it: eleven readings in twelve are interpolated std between anniversaries, because the 算出方法書 that would give the real within-year rule is unpublished REG-R2. 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. 1.48% cumulative probability against an amount at risk that starts at 1.85 times the maturity benefit. Omitting it understates the liability by 0.65% 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. It is also what makes the education cell’s death benefit switch limbs 85 months in 264 on this grid, where the annual grid never switched at all.

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 ¥3,988.78 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 the end of month t = 12n − 1, whose closing instant is anniversary n, the survivors are paid S with probability 1 R10 [S2] [S8]. Modelling maturity as a rate, or letting the projection run past t = 12n − 1 on a terminal age imported from the whole-life chassis, is wrong in both directions.

• Surrender must be suppressed in the final month, and only in it. A surrender at the close of the last month and the maturity payment fall at the same instant 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. On the monthly grid the carve-out is t = 12n − 1 alone: suppressing the whole final year, as an annual grid necessarily did, deletes eleven months of genuine surrender and overstates the maturing fraction — which is exactly the 0.5042 → 0.4949 move the conversion produced on the anchor cell.

• The policy value must converge on the maturity benefit. pol_val_pp(n) == sum_assured exactly at the final anniversary, 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/12⌋; every benefit runs on the 被保険者’s at x + ⌊t/12⌋ [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 12m. Every waiver trigger is conditional on the event falling during 保険料払込期間 [S1] [S10]. The premium-paying months are t = 0 … 12m − 1, so carrying q_pm to t = 12m and beyond moves policies out of the paying state the contract leaves in it, and does so in exactly the years when 86% of the second cell’s receipts fall.

• The three clocks are not interchangeable. t counts months from 0; k is an anniversary in years with k = 0 at issue; u is an elapsed month at which a value is read, u = t + 1 for the flows of month t. Reading a value cells at t rather than at t + 1 gives the row its opening balance and silently misstates every surrender benefit, every 学資 death benefit and every staged claim; reading cv_pp(t) where cv_at_m(t + 1) is meant is worse, because it is off by a factor of twelve in the index and still returns a plausible number. SC(0), W(n) = S and the schedule’s 3 / 6 / 12 / 15 / 18 / 20 are all on the k clock in years, and none of them moved when the projection index became a month.

• Only the projection index became monthly. The contractual constructions did not: the policy value, the surrender charge, the surrender value, the loan balance and the staged schedule are all defined at the 年単位の契約応当日 and all stayed annual. Converting them to a monthly recursion would invent a within-year rule the 算出方法書 does not publish REG-R2; what the model does instead is read them between anniversaries by a declared interpolation and agree with them exactly at every anniversary.

• 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(⌈u/12⌉, 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 anniversaries k = 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, and on this grid both bind. On the annual grid the reserve limb dominated at every anniversary and the max never switched. Read month by month it switches 85 times in 264: the premium limb steps up by a whole 年払 premium in each anniversary month and the value accretes through the year to overtake it, so the refund limb binds early in each policy year and the value limb late in it, until the value pulls clear for good in policy year 13. Hard-coding either limb is right eleven months a year at best — and the annual grid could not have told anyone that [S3] [S13].

• 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 it sits below the carrier’s own published 年払 figure [S11] [S16]. It did not move when the grid did, and it should not have: ρ is a ratio of contractual amounts, not of projected ones.

• 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 0.70 suppression multiplier, its step at m, or its 15% surrender spike models a product that does not exist here.