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) into a reference liability cash-flow projection on paper. They describe no single insurer’s contract. [S#] and [R#] resolve against sources.md in this directory, numbering carried verbatim from _research/income-guarantee.md and frozen; [REG-R#] resolves against references/regulatory-and-actuarial-references.md, whose own R-numbering is distinct and must never be read across. std marks a standardization introduced for the reference implementation; unverified marks a claim not confirmed against a retrieved document. Every contractual parameter here is identical to product-spec.md’s. Two parameters are new, and both are named as such where they appear: a rate-class mortality factor, which product-spec.md footnote 6 explicitly defers to this file because no carrier publishes the premium differential between classes, and a per-instalment annuity administration expense, which the chassis has no need of because the chassis pays a lump sum.

This is a death benefit. Survivor income term (shūnyū hoshō hoken, 収入保障保険) pays on the death of the insured, or on the contractual severe disability state (kōdo shōgai jōtai, 高度障害状態) treated as its accelerated equivalent, and pays it as a monthly income. It is not income protection in uklib’s sense; uklib’s IP_UK_S insures disability. Nothing in this file models a disability decrement.

This file states deltas. The term life technical notes (定期保険) are the library’s protection chassis, implemented in Term_JP_A. Inherited unchanged and not restated here: the decrement recursion and its processing order, the premium chassis, the std mortality construction with its 0.80 best-estimate factor, the lapse table, the expense and commission levels, the age last birthday (man-nenrei, 満年齢) / age nearest birthday (hoken-nenrei, 保険年齢) age-basis reconciliation, and the treatment of 高度障害 as one decrement with death. What changes: a monthly grid, a benefit that is an annuity-certain rather than a lump sum, a premium stream that stops on the annuity event while the benefit stream runs on, and a projection horizon that is longer than the policy term.

Model scope and conventions#

  • Purpose. Project gross best-estimate liability cash flows — premiums, the death and 高度障害 annuity instalments, claim expenses, annuity administration expenses, maintenance 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 the 基準日 rather than locked in at issue REG-R15. The same projection is the shape of the item-1 income-and-outgo analysis (ichi-gō shūshi bunseki, 1号収支分析) REG-R22.

  • Discounting, MOCE, required capital and reserving are out of scope, cited and not reproduced (see Valuation and reserve pointers). jplib computes no ratio and builds no policy reserve (sekinin-junbikin, 責任準備金). The omission matters more on this product than on any other protection product in the library, and Key sensitivities quantifies why.

  • Projection frequency. Monthly — the model is IncomeTerm_JP_S. The grid is not a refinement here, it is the contract: the benefit is one instalment per monthly payment date [S1 第3条第2項] [S5], the instalment count is a month count [S5] [S14] [S15], and the minimum payment guarantee period (saitei shiharai hoshō kikan, 最低支払保証期間) is stated in years but binds in months. An annual grid cannot represent max(N − m + 1, G) without inventing a within-year convention for both m and G.

  • Timing conventions std. Premium at the start of each policy month, in advance, on the in-force population only; maintenance expense at the start of the month; acquisition expense and initial commission at issue. Claims arise at the end of the month, and the claim expense with them. The first annuity instalment falls at the end of the month of the insured event and each later instalment at the end of each later month — the contractual timetable is the day before the first monthly policy anniversary falling on or after the event, then the day before each subsequent anniversary [S1 第3条第2項] [S5], which on a monthly grid is exactly one payment per month starting in the month of the event. Lapse at the end of the month, after deaths. Premium frequency is a timing feature, not an inert flag std: on 半年払 and 年払 the premium falls as 12 / f months’ premium at the start of each payment period and nothing in between, with no 前納 and no frequency discount applied because the discount is insurer-set and unpublished [S1 第14条] — so a policy year costs the same at all three frequencies and only the timing moves. The worked example is 月払, the frequency the only published rate grid is quoted in [S6].

  • Age basis std. Issue age (keiyaku nenrei, 契約年齢) is 満年齢 with the fraction truncated [S1 第37条] [S14]; attained age in month t is x + floor((t − 1) / 12). 生保標準生命表2018（死亡保険用）is built for a 保険年齢 basis REG-R20 R2, so reading it at 満年齢 reads it half a year early and understates mortality. The chassis states the bias and the optional sqrt(q_x · q_{x+1}) shift; both apply here unchanged.

  • Currency. JPY throughout [S1]. No FX layer.

  • Model points. Single-policy, on an expected (probability-weighted) basis. The anchor cell of the worked example is point_id = 1.

  • Termination — and the sentence this product exists to force. The policy terminates at the end of the policy term (hoken kikan, 保険期間) with nothing payable on survival: no 満期保険金, no surrender value (kaiyaku-henreikin, 解約返戻金) at any duration [S2] [S5] [S6] [S7] [S9] [S15]. But cash flow does not stop there. Where the insured event falls so late that fewer than G months remain, the annuity payment period is extended past the expiry date until the guarantee has run [S1 第3条第2項] [S3 第3条第3項] [S5] [S12] [S14]. The projection horizon is therefore

    T = N + G − 1

    months, not N. On the anchor cell N = 420 and G = 24, so T = 443: a death in policy month 420 pays its twenty-fourth instalment in month 443, twenty-three months after cover ended. Terminating the projection at t = N truncates real, contractual liability, and it is the single easiest error to make in an implementation of this product.

  • Contract boundary. Unlike the chassis, this contract has no renewal (kōshin, 更新) in any retrieved document [S5] [S6] [S8], and the premium is level and guaranteed for the whole 保険期間 with no review mechanic [S1] [S2] [S5] [S6] [S8] [S12]. The insurer therefore has no unilateral repricing right, the boundary is the full term, and the boundary argument that dominates the term life technical notes (定期保険) does not arise here. The run-off tail in months N + 1 … T is inside the boundary: it is the settlement of a claim that arose inside it.

  • Rounding. Intermediates at full precision; displayed cash flows to two decimals of a yen; in-force to six decimals; the claim and annuity-ledger populations to nine decimals std. Nine is not decoration: on a monthly grid at age 30 the monthly claim probability is about 3.2e−5, so six decimals leaves the first policy year’s claim and ledger populations with two significant figures — D(1) = 0.000031739 displays as 0.000032, a 0.8% distortion of the largest single component of the benefit, and the twelve months of policy year 1 collapse onto four distinct displayed values.

Model point attributes#

Attribute

Type

Anchor cell (point_id = 1)

sex

enum {M, F}

M

issue_age (x)

int, 満年齢, 20–70 [S6] [S7] [S14]

30

expiry_age

int, 45–90 [S8]; 歳満了 only, no 年満了 and no 更新 [S5] [S6]

65

term_m (N)

int months, 12 × (expiry_age − issue_age) — derived

420

guar_m (G)

int months, from {24, 60} [S3] [S5] [S7] [S9] [S12]

24

annuity_mth (A)

JPY/month, ¥50,000 minimum in ¥10,000 steps [S6] [S8] [S12]

150,000

rate_class

enum {非喫煙者優良体, 喫煙者優良体, 非喫煙者標準体, 喫煙者標準体} [S2] [S5] [S14]

非喫煙者優良体

class_factor

float, mortality multiplier for the class

0.70 std

premium_monthly (P_m)

JPY/month

2,565 [S6]

premium_mode

enum {monthly, semiannual, annual} [S1 第12条]

monthly

commutation

bool (一括受取 at the claim date; base run false)

false

living_needs

bool (リビング・ニーズ特約; base run false)

false

wop

bool (保険料払込免除; base run false)

false

reinstatement

bool (復活 module; base run false)

false

P_m is a published figure: ¥2,565 is the 65歳満了 / 保証2年 / 非喫煙優良体型 / 年金月額¥150,000 monthly rate for a male aged 30, as at 2025年12月2日 [S6]. Two honest qualifications carried over from product-spec.md footnote 7: the publishing carrier runs a two-class structure, so its 非喫煙優良体型 is not exactly the composite’s 非喫煙者優良体 cell, and the total-benefit illustration the cell is checked against is written on a 5年 guarantee by a different carrier [S14], which changes nothing before the last two policy years. std here covers the choice of cell and nothing else about the premium.

term_m is derived, not an input: every published contract example sets the term as to a stated attained age (sai manryō, 歳満了) [S2] [S5] [S6] [S8] [S9] [S12] [S14] [S15] [S17]. A model point supplying an n-year term is describing a product the composite does not have.

State variables#

Variable

Description

Updated

l(t)

In-force probability at the start of month t; l(1) = 1; l(t) = 0 for t > N

monthly recursion

q(t)

Best-estimate annual death-and-高度障害 rate (one decrement) at attained age

assumption lookup

q_m(t)

Monthly equivalent, 1 − (1 − q(t))^(1/12)

derived

w(t), w_m(t)

Annual and monthly ordinary lapse rate

assumption lookup

D(t)

Expected new claims in month t = l(t) × q_m(t)

monthly

R(t)

Annuity streams in payment during month t — the in-payment ledger

monthly recursion

CF(t)

Net cash flow of month t, insurer perspective (+ = inflow)

monthly

R(t) is the state variable this product adds to the chassis, and it obeys a rule that has no analogue anywhere else in jplib:

The in-payment ledger is never decremented. Not by the insured’s mortality — the insured is dead, and that is what opened the stream. Not by the recipient’s mortality — on the composite the instalments carry no survival condition [S1] [S5] [S14], so the stream is an annuity-certain. Not by lapse — a policy in claim cannot lapse, and premiums have ceased [S1 第12条第2項] [S3 第5条] [S8]. R(t) falls only when a stream reaches its contractual last instalment.

There is deliberately no cv_pp and no account value: the composite has no 解約返戻金 for the whole term [S2] [S5] [S6] [S7] [S9] [S15], and with no cash value there is no automatic premium loan (jidō furikae kashitsuke, 自動振替貸付) and no 契約者貸付 — one carrier states the absence in terms [S2]. Grace to 失効 to 復活-or-not is the whole persistency machinery, exactly as on the chassis.

Two contractual clocks are tracked and not monetized in the base run: the three-year suicide 免責期間 and the two-year 告知義務違反 contestability window, both running from the 責任開始期 and both restarted only by 復活 [S1] [S3] [S4] [S5] REG-R34 REG-R35.

Assumption inputs#

Three classes, kept separate.

(a) Contractual / guaranteed elements (cited)#

Input

Value

Basis

Survivor annuity (izoku nenkin, 遺族年金)

A per month from the insured event to the 保険期間満了日, extended where the guarantee requires

[S1 第3条] [S3 第3条] [S5] [S9] [S12] [S14]

高度障害年金

The same A, same timetable, same guarantee; mutually exclusive with the death annuity

[S1 第3条] [S3 第3条] [S5] [S9]

Instalment count

n_pay(m) = max(N − m + 1, G)

derivation below; [S5] [S14] [S15]

Guarantee mechanic

A term extension past expiry, not a benefit floor inside the term

[S1 第3条第2項] [S3 第3条第3項] [S5] [S12] [S14]

Survival condition

None; the stream is an annuity-certain

[S1] [S5] [S14]

Premium

Level for the whole 保険期間; 保険料払込期間 = 保険期間; no review, no 更新

[S1] [S2] [S5] [S6] [S8] [S12]

Premium cessation

On the annuity event: no further premium once the annuity begins

[S1 第12条第2項] [S3 第5条] [S8]

解約返戻金

None, whole term

[S2] [S5] [S6] [S7] [S9] [S15]

Grace (yūyo kikan, 猶予期間), 月払

To the last day of the month after the 払込期月; then 失効

[S1 第15条] [S3] [S4]

復活

3 years from lapse, on fresh underwriting and arrears with interest; rate class carries over

[S1 第17条] [S3] [S5]

Suicide 免責

3 years from the 責任開始期, reset on 復活; 責任準備金 paid to the owner

[S1] [S3] [S4] [S5]

Commutation (一括受取)

Present value of unpaid instalments, in whole, in part, or as the residue

[S2] [S3] [S5] [S7] [S10] [S12] [S14]

Residual floor

A partial commutation leaving 年金月額 below ¥50,000 is refused

[S7] [S1 第5条第3項] [S3 第6条第4項]

Benefit cap

年金現価保険金額 ¥300,000,000 — a cap on the present value

[S8]

リビング・ニーズ特約

年金現価 of the designated 年金月額 less 6 months’ interest and premium; cap ¥30,000,000; barred in the final year

[S2] [S5] [S7]

保険料払込免除

不慮の事故 on or after 責任開始期, 別表4 state within 180 days; disease-based waiver is a rider only

[S1 第6条] [S3 第8条] [S5] [S6]

Deriving the instalment count. With N the term in months, m the policy month of the insured event and G the guarantee in months, n_pay(m) = max(N − m + 1, G) reproduces every published illustration in the source set. On N = 420: 420 instalments for m = 1, 240 for m = 181, 60 for m = 361 [S14]; 411 for m = 10 and 178 for m = 243 [S15]; and on a 5年 guarantee, 420 for m = 1, 246 for m = 175, and 60 for a death 33 years in, where the remaining term is 24 months and the guarantee binds [S5]. Carriers label elapsed duration inconsistently — one counts the month of the event, another counts completed months — but the guarantee case is the only one where the two conventions could not both hold, and it holds.

The stream opened in month m therefore pays its last instalment in month

  ends_at(m) = m + n_pay(m) − 1 = max(N, m + G − 1)

which is the whole guarantee mechanic in one expression, and the expression a test should assert. For m ≤ N − G + 1 every stream ends at exactly N; only later claims run past it.

(b) Insurer-discretionary current elements#

Input

Snapshot value

Basis

契約者配当

Nil — every retrieved product is 無配当

[S1 第39条] [S2] [S5] [S15]

Commutation basis

Annuity-certain at 0.65% p.a. effective, monthly in arrears

std (1)

前納 discount, 高額割引

Insurer-set and unpublished; not modeled

[S1 第14条] [S6]; scope std

Pricing basis (assumed interest rate (yotei riritsu, 予定利率), 予定死亡率, 予定事業費率)

Not published for any 収入保障 contract in the set; filed under 保険業法第4条第2項第4号 and not public

REG-R2; gap

  1. The most important std number in this product, and the best-evidenced. No direct writer publishes the discount basis; the wordings are 「年金月額に所定の係数を乗じた額」 [S6] and 「将来に発生する利息を差し引いて算出した現在の保険契約の価値」 [S10]. One 特約条項 publishes the factor tables themselves — 年金の現価相当額 = 基本年金額 × a tabulated rate with no dependence on the annuitant’s age or sex, running 4.975 at a 5-year payment period, 9.801 at 10, 14.474 at 15, 18.997 at 20, 23.377 at 25, 27.616 at 30 and 39.542 at 45 [S13 別表1]. Fitting an annual annuity-due less a small constant to those gives about 0.61% p.a., and the second column of the same table, for a different main contract, about 1.45%; both fits are derivations recorded in _research/income-guarantee.md, not published rates, and the constant is part of the derivation — a plain annuity-due with no constant fits the same seven factors at 0.59%. Three carriers publish a worked commutation amount instead: ¥100,000 × 180 to ¥16,594,260 [S6], ¥200,000 × 300 to 約¥55,310,000 [S10] and ¥100,000 × 300 to 約¥27,640,000 [S17] — ratios of 0.92190, 0.92183 and 0.92133, implying 1.10%, 0.66% and 0.66% respectively. The two independent anchors — 0.61% from the factor table and 0.66% from the two 300-instalment amounts — have a midpoint of 0.635%; the composite takes that rounded to the nearest 0.05%, 0.65% p.a. effective. Verified numerically at that rate, monthly in arrears: ¥200,000 × 300 commutes to ¥55,377,890.69 (+0.12% on the published 約 amount) and ¥100,000 × 300 to ¥27,688,945.35 (+0.18%), both inside the published rounding. It does not reproduce the 180-instalment amount: at 0.65% that stream commutes at ¥17,148,368.65, a ratio of 0.952687 against the published 0.921903. That is a fact about the data, not a failure of the fit — no single flat rate produces a near-constant ratio at both 180 and 300 instalments, so either the carriers’ bases differ or a term-dependent adjustment is in use, and neither is published. Observed range to test over: 0.61%–1.45%.

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

Mortality — one decrement. 生保標準生命表2018（死亡保険用）includes 高度障害 inside its death rate R2 REG-R20, and the contract pays one annuity and the other is then not payable [S1 第3条第3・4項] [S3 第3条第6・7項]. Death and 高度障害 are therefore one decrement carrying one benefit. The table is freely readable at a stable public URL R1 REG-R18 but its publisher prohibits reproduction and transmission without written consent REG-R21, so the library cites the table, quotes the rates the worked example needs, and ships mort_table.csv as a std construction whose provenance column points at the IAJ entries.

Step

Rule

Basis

Anchors verified for this product

Male 死亡保険用 q30 = 0.00068, q60 = 0.00653, q65 = 0.01015, q80 = 0.05006; female q60 = 0.00363

read from the table R1 REG-R18

Anchors carried from the chassis

Male q35 = 0.00077, q40 = 0.00118, q50 = 0.00285, q90 = 0.15760; female q30 = 0.00037

term life technical notes (定期保険)

Shipped anchors

The union of every anchor any jplib product reads from the table: both sexes at ages 20, 22, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80 and 85, plus male 31–34

one canonical std file, so a cell carries the same value and the same provenance in every product that ships it

Female rates

Read at the female anchors in their own right, not built as a ratio to the male rate

R1 REG-R18

Interpolation

Log-linear in ln q between the two neighbouring anchors, rounded to 5 decimals; no extrapolation anywhere, because every shipped age lies between two sourced anchors

std

Best estimate

q(t) = 0.80 × class_factor × q_x^tab

chassis 0.80 std; class factor std (2)

Monthly conversion

q_m = 1 − (1 − q)^(1/12)

std

Improvement

None in the base run

std

  1. The rate-class factor is the parameter product-spec.md footnote 6 defers to this file. The composite has four classes [S2] [S5] [S14], their qualification is published and measured rather than declared — BMI 18.0 to under 27.0, 最大血圧 under 140 and 最小血圧 under 90 mmHg, no tobacco in the past year, verified by a cotinine (コチニン) test [S2] [S5] — and no carrier publishes the premium differential between them. The reference set is therefore wholly std, given a stated internal structure rather than four free numbers:

    Class

    class_factor std

    非喫煙者優良体

    0.70

    非喫煙者標準体

    0.90

    喫煙者優良体

    1.05

    喫煙者標準体

    1.35

    The structure is a smoker/non-smoker ratio of 1.50 and a preferred/standard ratio of 0.778, applied consistently in both directions, and the levels are pinned by one arithmetic constraint: 生保標準生命表2018 is an all-lives basis, so the mix-weighted mean of the four factors must be 1.00 or the class split silently re-levels the whole table. An illustrative mix of 25% / 35% / 10% / 30% gives exactly 1.000:

    0.25 * 0.70 + 0.35 * 0.90 + 0.10 * 1.05 + 0.30 * 1.35 = 1.000

    The mix is std and illustrative; it is used to check the normalization and is not a claim about the market. No observed range can be given, because nothing is published.

Lapse. The chassis table, unchanged and reconciled there to the LIAJ’s FY2024 個人保険 解約・失効率 of 5.6% REG-R31:

Policy year

1

2

3

4

5+

Annual w(t) std

9%

7%

6%

5.5%

5%

with w_m(t) = 1 − (1 − w(t))^(1/12) std. Lapse pays nothing: there is no 解約返戻金 [S2] [S5] [S6] [S7] [S9] [S15]. Nothing product-specific was found — the national household survey does not break 収入保障保険 out at all R11 REG-R32 — so this table is the chassis’s table used because it is the only one the library has, not because it was calibrated here.

Expenses and commission. All chassis levels, unchanged, plus one new item.

Input

Value

Note

Acquisition expense E0

¥15,000 per policy at issue

chassis std

Initial commission c0

50% of the first-year annualized premium

chassis std

Renewal commission c_r

5% of premiums from month 13

chassis std

Maintenance e_m(t)

¥4,000 p.a. inflating 1.0% p.a., taken as 4,000 / 12 per month

chassis std

Claim expense ec

¥30,000 per claim, once, when the stream opens

chassis std

Annuity expense ea

¥200 per instalment paid

new std (3)

  1. The chassis pays a lump sum and closes the file. This product pays up to 420 instalments over up to 35 years after the claim, and the administration of that stream is a real cost that no cited document quantifies. ea is charged against the ledger R(t), not against l(t) — it is the one expense that survives the end of the policy term. The level is a std placeholder; its cash-flow weight on the anchor cell is small (¥591.08 undiscounted per policy issued against ¥443,313.69 of claims) but its structure is the point: an implementation that attaches every expense to l(t) charges nothing at all in months 421–443, when instalments are still being paid.

Cash flow components and recursions#

Notation#

Symbol

Meaning

cells

t

policy month, t = 1 .. T

—

x

契約年齢 (満年齢); attained age in month t is x + floor((t − 1) / 12)

age

y(t)

policy year, 1 + floor((t − 1) / 12)

policy_year

N

保険期間 in months, 12 × (expiry_age − x)

term_m

G

最低支払保証期間 in months

guar_m

T

projection horizon in months, N + G − 1

proj_len

A

年金月額, JPY per month

annuity_mth

P_m

monthly office premium, JPY per month

premium_mth_pp

P_due(t)

office premium falling due at the start of month t

prem_due_pp

n_pay(m)

instalments generated by a claim in month m, max(N − m + 1, G)

pay_count

ends_at(m)

month of that stream’s last instalment, max(N, m + G − 1)

pay_end

q(t), q_m(t)

annual and monthly death-and-高度障害 rate

mort_rate, mort_rate_mth

w(t), w_m(t)

annual and monthly ordinary lapse rate

lapse_rate, lapse_rate_mth

l(t)

in-force probability at the start of month t

pols_if

D(t)

expected new claims in month t, l(t) × q_m(t)

pols_death

R(t)

annuity streams in payment during month t

annuities_if

E0, c0, c_r

acquisition expense; initial commission; renewal commission rate

expense_acq, commissions

e_m(t)

monthly maintenance, (4,000 / 12) × 1.01^(y(t) − 1)

expenses

ec, ea

claim expense per claim; annuity expense per instalment

expense_claim, expense_annuity

i_c, v

commutation rate p.a. effective; v = (1 + i_c)^(−1/12)

commute_rate

CF(t)

net cash flow of month t (+ inflow)

net_cf

Dimensional check. q, q_m, w, w_m, l, D, R are dimensionless — l and D are probabilities per policy issued, and R is a count of instalments falling due, also per policy issued, so it is dimensionless in the same sense and is not a population of policies. A, P_m, e_m, ea are JPY per month; E0, c0, ec are JPY per event; n_pay and ends_at are month counts. Every term of CF(t) is JPY per month per policy issued. The two products that must not be confused: A × R(t) is JPY per month (annuity outgo) while A × n_pay(m) is JPY (the total benefit for one claim).

The in-payment ledger#

The ledger is the whole model. For t = 1 .. T:

R(t) = R(t−1) − ended(t) + D(t),        R(0) = 0

ended(t) = sum of D(s) over all s with ends_at(s) = t − 1

D(t) enters R(t) in the same month, because the first instalment falls at the end of the month of the event. Two cases exhaust ended(t):

ended(t) = sum of D(s) for s = 1 .. N − G + 1     if t = N + 1
         = D(t − G)                               if t > N + 1
         = 0                                      otherwise

The first case is the structural fact worth a test: every stream opened in months 1 … N − G + 1 pays its last instalment in month N exactly, whenever it opened, because the expiry date is fixed at issue. It follows immediately that

R(N) = sum of D(s) for s = 1 .. N

— the ledger at the last month of cover equals every claim the contract has ever made. Two further identities a model must satisfy:

R(t) = sum of D(s) over s with s <= t <= ends_at(s)          (direct form)
sum over t of R(t) = sum over s of D(s) * n_pay(s)           (total instalments)

check_annuity_ledger() asserts the recursion against the direct form at every t and returns a single bool.

Processing order#

For t = 1 .. T, in this order std:

  1. Start of month — income and standing outgo, on the in-force population only. Premium P_due(t) × l(t); maintenance e_m(t) × l(t); renewal commission c_r × P_due(t) × l(t) for t ≥ 13. At t = 1 additionally E0 + c0 per policy issued (l(1) = 1). For t > N all four are zero: cover has expired and l(t) = 0. P_due(t) is the premium falling due in month t, which on the anchor cell’s 月払 is P_m every month; see the frequency rule in Timing conventions.

  2. Decrement lookup. q(t) at attained age x + floor((t − 1) / 12); q_m(t) from it; w(t) from the lapse table by y(t); w_m(t) from it. For t > N, all zero.

  3. End of month — new claims. D(t) = l(t) × q_m(t). Claim expense ec × D(t). No lump sum is paid. The claim opens an annuity stream; it does not settle one.

  4. End of month — the ledger. R(t) = R(t−1) − ended(t) + D(t). Annuity outgo A × R(t); annuity expense ea × R(t). This step runs for every t up to T, including the months after the policy term has ended.

  5. End of month — ordinary lapse. l(t) × (1 − q_m(t)) × w_m(t) leave, applied to survivors of mortality. Nothing is paid.

  6. Roll forward.

    l(t+1) = l(t) * (1 - q_m(t)) * (1 - w_m(t))     for t < N
l(t+1) = 0                                       for t >= N

    The identity l(t) − l(t+1) = D(t) + lapses(t) holds for t < N, and check_pols_roll_fwd() asserts it over all such t. At t = N the survivors leave with nothing: on the anchor cell that is 0.144342 of the original cohort.

Net cash flow#

CF(t) = P_due(t) * l(t)                        (premiums)
      - A * R(t)                               (annuity instalments)
      - ea * R(t)                              (annuity administration)
      - ec * D(t)                              (claim expense)
      - e_m(t) * l(t)                          (maintenance)
      - c_r * P_due(t) * l(t) * 1{t >= 13}     (renewal commission)
      - (E0 + c0) * 1{t = 1}                   (acquisition)

net_cf is income-positive, per the library convention. Lapse contributes no term: it acts only through l(t), and claims_lapse is identically zero — the zero is the product fact worth publishing. Note which population multiplies which term: premiums, maintenance and commission carry l(t); the annuity instalments and the annuity expense carry R(t); and l(t) and R(t) are disjoint populations that must never be added.

Optional modules (all off in the base run)#

The numeric values, first. Each module below is switched off in the base run, so none of these numbers touches the worked example — but the std rule is that a quantitative parameter is written down with its rationale wherever it lives, not left to be read off the model. Four rows are contractual and cited (ln_defer_m, ln_cap, reinst_window_m, and commute_rate through its own footnote); no retrieved document quantifies any of the other seven, so no observed range can be given for them. The “why this value” column says what each number is chosen to do; a user switching a module on should replace the row rather than calibrate to it.

Module

Parameter

Value std

Why this value

リビング・ニーズ特約

ln_take_up

5% of the month’s claims

A visible but non-dominant election, chosen so the module changes the claim mix without swamping it. The rider’s presence is sourced [S2] [S5] [S7]; only the take-up is invented

リビング・ニーズ特約

ln_defer_m

6 months

Contractual, not chosen: the payout is the 年金現価 less six months’ interest and premium equivalent [S2] [S5] [S7]

リビング・ニーズ特約

ln_cap

¥30,000,000

Contractual [S2] [S5] [S7]

保険料払込免除

wop_inc_rate

0.06% p.a.

An order of magnitude below q(t) at the older ages the waiver bites at, because 別表4 is a lower bar than 別表3 but the trigger still requires an 不慮の事故 plus a 180-day survival — a deliberately separate rate, so that no reader mistakes it for the 高度障害 incidence

保険料払込免除

wop_rec_rate

10% p.a.

A mean stay of about ten years in the waived state: the 別表4 states are permanent impairments, so recovery is slow rather than absent, and a zero recovery rate would make the waived fraction monotone and hide the two-state structure

復活

reinst_rate

15% of each month’s lapses

Below the mid-range of what a three-year 復活 window could deliver, on the view that a 無解約返戻金型 policy gives an owner nothing to protect by reinstating. It is a single-lag approximation, so this rate carries the whole window’s take-up

復活

reinst_lag_m

6 months

One lag standing for the whole three-year window, set at the point where arrears are still small enough to be paid in one instalment. The model rejects a lag outside reinst_window_m by name

復活

reinst_window_m

36 months

Contractual: 復活 runs three years from lapse [S1 第17条] [S3] [S5]

復活

reinst_int_rate

0.65% p.a.

復活 requires arrears with interest [S1 第17条], and no carrier publishes the rate. Set equal to commute_rate, the one interest basis this product has any published evidence for, rather than introducing a second unevidenced rate

Selective lapsation

sel_lapse_lambda

0

Off in the base run; the mechanism is real but unquantified (Policyholder behavior modeling)

Selective lapsation

sel_lapse_ref

1.0

The threshold l_ref is expressed as a fraction of the original cohort, so 1.0 makes the loading start at issue and grow as the cohort runs off. It has no effect while λ = 0

一括受取

commute_rate

0.65% p.a. effective

The one std number here with published anchors; assumption class (b) footnote 1 carries the derivation and the 0.61%–1.45% observed range

  • Commutation (一括受取). With commutation = true, a claim in month m is settled at the claim date by a lump sum instead of the stream:

    L(n) = A * v * (1 - v^n) / (1 - v),    v = (1 + i_c)^(-1/12),  n = n_pay(m)

    at i_c = 0.65% std. The ledger is then not opened and the annuity expense collapses to one payment. On the anchor cell a death in month 1 commutes ¥63,000,000 of instalments to ¥56,352,381.90, a ratio of 0.894482; at 300 remaining instalments the ratio is 0.922965, against the 0.92133–0.92190 the three published illustrations show [S6] [S10] [S17]. Contractually a full commutation extinguishes the contract [S1 第5条第2項] [S3 第6条第3項] [S12] [S14], so in a projection it changes the shape of the claim payment and nothing else. Partial commutation (一部一括受取) is not modeled: it is barred once the first instalment has been paid [S3 第6条第4項第1号], limited to once during the term at two carriers [S10] [S12], and refused where the residual 年金月額 falls below ¥50,000 [S7] — three restrictions that make it an election on a claim already open rather than a cash-flow shape [std scope].

  • リビング・ニーズ特約. Acceleration incidence std (no retrieved document gives one). The payout is the 年金現価 of the designated 年金月額 less six months’ interest and premium equivalent, capped at ¥30,000,000 and barred in the final year [S2] [S5] [S7]. The product-specific consequence: because the amount is the present value of an income stream, the cap binds far earlier in the term than it does on a level sum assured — on the anchor cell the full 年金現価 is ¥56,352,381.90 at issue, so the cap bites from month 1 and keeps biting until the unpaid stream has run down below ¥30,000,000 of present value.

  • 保険料払込免除. A waiver state on the accident-plus-180-days-plus-別表4 test [S1 第6条] [S3 第8条] [S5] [S6] with std incidence. 別表4 is a materially lower bar than the 別表3 高度障害 schedule, so the waiver incidence is not the 高度障害 incidence and must not reuse q(t).

  • 復活. The chassis’s lapsed-but-reinstatable population with a three-year window [S1 第17条] [S3] [S5] and a std reinstatement rate. Off in the base run. The rate class carries over unchanged on reinstatement [S3], which matters here because the class is a mortality parameter.

  • Recipient-mortality variant. One carrier alone conditions second-and-later instalments on the recipient being alive [S3 第3条第3項], commuting the residue to the 法定相続人 on the recipient’s death [S3 第7条]. Modeling it requires a post-event mortality basis on a life the contract never underwrote, and the 年金開始後用 table stays on the 2007 vintage REG-R11 — a whole second basis for one carrier’s wording. Out of scope std, and the contract side confirms the composite’s choice: the one published factor table depends on the payment period and the type of main contract and explicitly not on the annuitant’s age or sex [S13 別表1]. That is a published statement that the stream is an annuity-certain.

Policyholder behavior modeling#

All dynamic formulas are std reference constructions.

  • No renewal decision. The chassis’s largest behavioural lever, the 更新 decline rate, is absent here — no retrieved document offers 更新, and one states the absence in terms [S5]. A model that imports the chassis’s d(t) invents a decision this contract does not have. Its nearest replacement is 保険契約の変換, conversion into a 定期保険 or 終身保険 without underwriting, blocked in the final two years [S6]; that creates a new contract on a different chassis at then-current rates, so it produces no liability on the modeled policy and is out of scope [std scope].

  • Selective lapsation std (optional). q_eff(t) = q(t) × [1 + λ × max(0, 1 − l(t)/l_ref)] with λ std and base run λ = 0. The mechanism is weaker than on the chassis because there is no periodic no-underwriting renewal to select against, but it is not absent: the rate class is fixed at issue and cannot be changed even if BMI, blood pressure or smoking status changes [S2] [S14], so a life whose health deteriorates keeps a preferred rate while a life whose health improves cannot get one and may re-shop.

  • Commutation take-up. Zero in the base run std. No carrier publishes an election frequency. The election is the recipient’s, not the policyholder’s, and it is made after the insured event, so it cannot be driven off any pre-claim behavioural variable.

  • 減額. Permitted above an insurer-set floor; on the 無解約返戻金型 composite it produces no refund at all [S1 第28条] [S3] [S7]. Not modeled: it changes A and P_m together, which is a model-point re-parameterization rather than a decrement [std scope].

  • クーリング・オフ. Out of scope: the model begins with cover in force and the eight-day statutory population REG-R36 already out. One carrier contracts for 14 days [S5].

Worked example#

Anchor cell (point_id = 1). Male, 契約年齢 30 (満年齢), 65歳満了 so N = 420 months, 最低支払保証期間 2年 so G = 24 months, T = 420 + 24 − 1 = 443 months, 年金月額 A = ¥150,000, rate class 非喫煙者優良体, 月払保険料 P_m = ¥2,565 [S6]. Base run: no commutation, no リビング・ニーズ, no waiver, no 復活, no selective lapsation.

Headline arithmetic, for orientation. A death in policy month 1 pays 420 instalments of ¥150,000 = ¥63,000,000 [S14]; total premium if the contract runs to expiry is ¥2,565 × 420 = ¥1,077,300, about 1.7% of that. A death in policy month 419 pays max(420 - 419 + 1, 24) = 24 instalments, running from month 419 to month 442 — twenty-two months past the expiry date.

Every assumption value the cell uses. The mortality anchor q30 = 0.00068 is read from 生保標準生命表2018（死亡保険用）男 R1 REG-R18; it is a sourced value, not an illustration. The best-estimate rate is q(t) = 0.80 × 0.70 × q_x^tab — the chassis’s 0.80 std factor and this product’s 0.70 std 非喫煙者優良体 class factor — so at attained age 30

q(t)   = 0.80 * 0.70 * 0.00068 = 0.000380800     (annual)
q_m(t) = 1 - (1 - 0.000380800)^(1/12) = 0.000031738873   (monthly)

Policy-year-1 lapse is 9% std, so w_m = 1 − 0.91^(1/12) = 0.007828420342. Expenses and commission, all std chassis levels: E0 = ¥15,000; c0 = 0.50 × 12 × 2,565 = ¥15,390; c_r = 5% from month 13; e_m(t) = (4,000 / 12) × 1.01^(y(t) − 1), so ¥333.333333 a month in policy year 1 and ¥336.666667 in year 2; ec = ¥30,000; ea = ¥200.

Further table rates used later in the projection. Three are themselves sourced anchors — q31 = 0.00069, q32 = 0.00070, q45 = 0.00177 R1 REG-R18 — and three are log-linear interpolations in ln q between the neighbouring anchors, rounded to 5 decimals std: q44 = 0.00163, q63 = 0.00851, q64 = 0.00929.

t

age

l(t)

Premiums

D(t)

R(t)

Annuity claims

Claim + ann. exp

Maint. + acq.

Comm.

CF(t)

1

30

1.000000

2,565.00

0.000031739

0.000031739

4.76

0.96

30,723.33

0.00

−28,164.05

2

30

0.992140

2,544.84

0.000031489

0.000063228

9.48

0.96

330.71

0.00

+2,203.68

3

30

0.984342

2,524.84

0.000031242

0.000094470

14.17

0.96

328.11

0.00

+2,181.60

13

31

0.909653

2,333.26

0.000029296

0.000394122

59.12

0.96

306.25

116.66

+1,850.27

420

64

0.145023

371.98

0.000063023

0.016779783

2,516.97

5.25

67.80

18.60

−2,236.63

421

—

0.000000

0.00

0.000000000

0.001463980

219.60

0.29

0.00

0.00

−219.89

443

—

0.000000

0.00

0.000000000

0.000063023

9.45

0.01

0.00

0.00

−9.47

Trace, month 1. l(1) = 1; premium = 2,565 × 1 = 2,565.00. D(1) = 1 × 0.000031738873 = 0.000031738873. The claim opens a stream and pays no lump sum, so R(1) = R(0) − 0 + D(1) = 0.000031738873 and annuity outgo = 150,000 × 0.000031738873 = 4.76083098. Annuity expense = 200 × 0.000031738873 = 0.00634777; claim expense = 30,000 × 0.000031738873 = 0.95216620; the two together are 0.95851397. Maintenance = 4,000 / 12 = 333.33333333; acquisition = E0 + c0 = 15,000.00 + 15,390.00 = 30,390.00, so the column shows 30,723.33333333. CF(1) = 2,565.00 − 4.76083098 − 0.00634777 − 0.95216620 − 333.33333333 − 30,390.00 = −28,164.05267828 → −¥28,164.05. Roll forward: l(2) = 1 × (1 − 0.000031738873) × (1 − 0.007828420342) = 0.9921400892.

Trace, month 2. Premium = 2,565 × 0.9921400892 = 2,544.83932893. q_m(2) = 0.000031738873 still — the attained age is unchanged for the first twelve months — so D(2) = 0.9921400892 × 0.000031738873 = 0.000031489408. R(2) = 0.000031738873 + 0.000031489408 = 0.000063228282: nothing ended, because the first stream runs to month 420. Annuity outgo = 150,000 × 0.000063228282 = 9.48424226 — already double month 1’s, on 0.99 of the population, because the ledger accumulates while l(t) decays. Annuity expense = 200 × 0.000063228282 = 0.01264566; claim expense = 30,000 × 0.000031489408 = 0.94468225. Maintenance = 333.33333333 × 0.9921400892 = 330.71336308. No commission before month 13. CF(2) = 2,544.83932893 − 9.48424226 − 0.01264566 − 0.94468225 − 330.71336308 = +2,203.68439568 → +¥2,203.68. Roll forward: l(3) = 0.9921400892 × (1 − 0.000031738873) × (1 − 0.007828420342) = 0.9843419567.

Trace, month 3. Premium = 2,565 × 0.9843419567 = 2,524.83711893. D(3) = 0.9843419567 × 0.000031738873 = 0.000031241905; R(3) = 0.000063228282 + 0.000031241905 = 0.000094470186; annuity outgo = 150,000 × 0.000094470186 = 14.17052794; annuity expense = 0.01889404; claim expense = 0.93725714; maintenance = 333.33333333 × 0.9843419567 = 328.11398557. CF(3) = 2,524.83711893 − 14.17052794 − 0.01889404 − 0.93725714 − 328.11398557 = +2,181.59645425 → +¥2,181.60.

Trace, month 13 — the first month of policy year 2. Three things change at once and an implementation can get any of them wrong. The attained age moves to 31, so q(13) = 0.80 × 0.70 × 0.00069 = 0.000386400 and q_m(13) = 0.000032205704. The lapse rate moves to the year-2 row, w = 7%, w_m = 0.006029308066. And maintenance inflates: e_m(13) = (4,000 / 12) × 1.01 = 336.66666667. With l(13) = 0.9096534720: premium = 2,565 × 0.9096534720 = 2,333.26115568; renewal commission = 0.05 × 2,333.26115568 = 116.66305778, the first one paid; D(13) = 0.9096534720 × 0.000032205704 = 0.000029296030; R(13) = 0.000364825643 + 0.000029296030 = 0.000394121674; annuity outgo = 150,000 × 0.000394121674 = 59.11825109; annuity expense = 0.07882433; claim expense = 0.87888091; maintenance = 336.66666667 × 0.9096534720 = 306.25000224. CF(13) = 2,333.26115568 − 59.11825109 − 0.07882433 − 0.87888091 − 306.25000224 − 116.66305778 = +1,850.27213932 → +¥1,850.27.

Trace, month 420 — the last month of cover. l(420) = 0.1450233243; premium = 2,565 × 0.1450233243 = 371.98482677, the four-hundred-and-twentieth and last. q(420) = 0.80 × 0.70 × 0.00929 = 0.005202400, q_m(420) = 0.000434570514, so D(420) = 0.000063022861. Nothing has ended yet, so R(420) = 0.016716760543 + 0.000063022861 = 0.016779783403 — and this is exactly the sum of D(s) over the whole term, because every stream is still paying in month 420. Annuity outgo = 150,000 × 0.016779783403 = 2,516.96751047; annuity expense = 3.35595668; claim expense = 1.89068582; maintenance = (4,000/12) × 1.01^34 × 0.1450233243 = 67.80212570; commission = 18.59924134. CF(420) = 371.98482677 − 2,516.96751047 − 3.35595668 − 1.89068582 − 67.80212570 − 18.59924134 = −2,236.63069323 → −¥2,236.63. Survivors leave with nothing: 0.1450233243 × (1 − 0.000434570514) × (1 − 0.004265318778) = 0.1443419995, and l(421) = 0.

Trace, month 421 — the first month past expiry, and the row a wrong model does not have. No premium, no maintenance, no commission, no new claims: l(421) = 0. Every stream opened in months 1–397 ended at month 420, so ended(421) = sum of D(s) for s = 1 .. 397 = 0.015315803299, and R(421) = 0.016779783403 − 0.015315803299 + 0 = 0.001463980104 — the streams from months 398–420, which the guarantee carries past expiry. Annuity outgo = 150,000 × 0.001463980104 = 219.59701556; annuity expense = 0.29279602. CF(421) = −219.59701556 − 0.29279602 = −219.88981158 → −¥219.89. From here ended(t) = D(t − 24), so the ledger runs down one month’s claims at a time until R(443) = D(420) = 0.000063022861 and CF(443) = −9.46603365 → −¥9.47. The projection ends at t = 443.

Totals over the 443 months, undiscounted, per policy issued.

Line

Amount

Premiums

¥461,030.83

Annuity instalments

¥443,313.69

Annuity administration

¥591.08

Claim expense

¥503.39

Maintenance

¥67,706.86

Commission (renewal)

¥21,577.36

Acquisition (E0 + c0)

¥30,390.00

Net cash flow

−¥103,051.56

Structural quantities behind those totals: expected claims over the term sum D(s) = 0.016779783; expected instalments sum R(t) = 2.955425 per policy issued, which reconciles exactly to sum D(s) × n_pay(s); average total benefit per claim ¥26,419,511.96; lapses over the term 0.838878 and survivors at expiry 0.144342 of the original cohort. ¥2,645.21 of the claim outgo — 0.5967% — falls in months 421 to 443, after the policy has expired.

Read the sign honestly. The undiscounted net is negative, and the reason is not a bug. The premium is a published preferred-non-smoker rate and the assumption basis is a std adjustment of a valuation table carrying a 2σ margin R2 REG-R20; the pricing basis that would reconcile them — 予定利率, 予定死亡率, 予定事業費率 — sits in the 算出方法書 filed under 保険業法第4条第2項第4号 and is not public REG-R2. More importantly, on this product an undiscounted total is close to meaningless: the benefit is paid over up to 35 years after a claim that itself arises over 35 years, so the claim leg discounts far harder than the premium leg. Present-valuing the same projection at flat annual effective rates gives −¥103,051.56 at 0%, −¥73,865.82 at 0.5%, −¥49,216.50 at 1% and −¥10,895.85 at 2%. Discounting is out of scope for the model and those four numbers are a diagnostic, not a result — but a reader who takes the undiscounted total as the liability has mis-read this product more badly than on any other in the library.

Valuation and reserve pointers#

This library projects gross 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). A conventional guaranteed 収入保障 contract is inside the regime: 保険業法第116条第2項 delegates the method and the coefficients REG-R4, and 施行規則第68条 excludes only separate-account-linked contracts, contracts with no 保険料積立金, contracts where the insurer has disclosed it may change the basis, and residually designated classes — none of which catches this product R8 REG-R7. 第69条 requires 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) per category R8 REG-R8. 平成8年大蔵省告示第48号 supplies the method — net level premium method (heijun jun-hokenryō-shiki, 平準純保険料式) — and the table vintage: contracts from 2018-04-01 value on 生保標準生命表2018（死亡保険用）REG-R10 REG-R11 R3. The discount rate is the standard valuation interest rate (hyōjun riritsu, 標準利率), which the supervisory guideline defines as 「責任準備金告示に規定する予定利率」 R9 REG-R10; its current numeric value could not be established from any retrieved document and is unverified — the 新旧対照表 attachments on the regulator’s page were not fetched R10.

  • The valuation table is not this model’s basis. 標準生命表2018 carries a ~2σ margin capped at 130% of the unadjusted rate plus a forward improvement allowance R2 REG-R20, while q(t) here is a std adjustment of it and is further multiplied by a std rate- class factor. Three separate departures from the statutory basis sit between this projection and a 責任準備金; say which basis is in use at every point.

  • ESR. From 2026-03-31 insurers report on the 経済価値ベースのソルベンシー規制: assets at fair value, liabilities as 現在推計 + MOCE, required capital at 99.5% over one year, early corrective action below ESR 100% REG-R15, replacing as the trigger the ソルベンシー・マージン比率 threshold of 200% REG-R17 REG-R15. jplib computes neither ratio. What the regime change means for this product is specific: a benefit whose amount is a function of when the claim occurs, settled over decades and re-discounted on a curve that moves at every 基準日, is far more interest-sensitive than a level sum assured, and a locked-in basis conceals that.

  • The professional use of this projection. 保険業法第121条第1項第1号 requires the 保険計理人’s 意見書 REG-R6; the IAJ practice standard turns it into the 1号収支分析 — a forward projection of premiums, claims, expenses and surrenders by 区分経理 segment over at least ten future years, sufficiency-tested over the first five REG-R22. Note the mismatch this product creates: a ten-year window on a 35-year contract sees only the earliest, largest instalment counts and none of the run-off tail.

  • Accounting. IFRS 17 is voluntary in Japan; IFRS applies as 指定国際会計基準 to insurers that elect it REG-R47. One projection feeds three measurement bases — J-GAAP REG-R10, ESR REG-R15 and IFRS where adopted — and conflating them gets wrong which assumptions are locked in.

  • On insurer failure, 生命保険契約者保護機構 covers up to 90% of the 責任準備金 under a rate delegated by 保険業法第270条の3 to ordinance REG-R40 REG-R41. Cited, never modeled.

  • Tax is not a model output but changes what the numbers mean. At the death the object taxed for 相続税 is the 年金受給権, valued at the greatest of the surrender value, the lump sum available in lieu, and the average annual amount times the 複利年金現価率 at the contract’s 予定利率 R6 R5; on a 無解約返戻金型 design the first limb is zero, so the commutation basis of assumption class (b) is also the tax valuation — the ¥300,000,000 年金現価 cap [S8] and the published factors [S13] are tax-relevant numbers. Instalments are then 雑所得 in part R4. On the premium side the contract sits in the 一般生命保険料 basket R7 REG-R43.

Key sensitivities and model risks#

In rough order of leverage on the anchor cell. Every figure below is the undiscounted net cash flow or claim outgo per policy issued, from the same projection.

  1. The rate-class mortality factor. class_factor = 0.70 std is the largest lever and the least evidenced parameter in the file, because no carrier publishes a class differential for this product [S2] [S5] [S6] [S14] [S16]. Annuity outgo runs ¥443,313.69 at 0.70, ¥568,289.70 at 0.90, ¥661,538.07 at 1.05 and ¥846,803.38 at 1.35 — a factor of 1.9 across the composite’s own four classes, on a premium the carrier quotes for the cheapest of them.

  2. The chassis’s 0.80 best-estimate factor. Annuity outgo is ¥426,306.73 at 0.769 (the arithmetic implied by removing a margin at its 130% cap REG-R20), ¥443,313.69 at 0.80 and ¥552,708.11 at 1.00 (the raw valuation table). Items 1 and 2 multiply: the two corners of the joint range give ¥426,306.73 (0.769 × 0.70) and ¥1,053,287.56 (1.00 × 1.35), a factor of 2.47, and no document narrows either input.

  3. Discounting, which this library does not do. Net cash flow is −¥103,051.56 undiscounted and −¥10,895.85 at 2% p.a. Nowhere else in jplib does the discount rate move the answer this far, because nowhere else is the benefit a 35-year stream beginning at an uncertain date. Any user comparing this product’s undiscounted output with the term life chassis (定期保険)’s is comparing two quantities of different economic meaning.

  4. The guarantee length. Annuity outgo is ¥440,668.48 with no guarantee, ¥443,313.69 at 2年, ¥457,179.73 at 5年 and ¥503,961.05 at 10年 — so the composite’s 2年 guarantee is worth 0.60% of claims, the 5年 alternative in the composite menu 3.7%, and the 10年 option one carrier publishes [S5] 14.4%, each measured against the no-guarantee run. The guarantee is cheap precisely because it binds only in the last G months of a 420-month term, where few lives remain. The 0-month and 120-month runs are outside the composite’s menu, so reproducing them means relaxing the model’s own guar_m validator; the 2年 and 5年 figures are the two shipped configurations.

  5. Lapse, whose sign is the opposite of the chassis’s. Net cash flow is −¥269,617.32 at zero lapse, −¥103,051.56 on the std table and −¥68,603.79 at 1.5× those rates. On this assumption set lapse relieves the liability, because expected claims exceed premiums; on a pricing basis it would not. A sensitivity whose sign flips with the basis needs both runs reported, not one.

  6. The commutation basis, if the module is on. Total claim outgo under full commutation at the claim date is ¥415,875.64 at 0.61%, ¥414,176.30 at the std 0.65% and ¥382,513.43 at 1.45% — the published range [S13] [S6] [S10] [S17] moves claim outgo by 8%, and the commutation module itself cuts claim outgo to 93.43% of the instalment total. Off in the base run, so the exposure is latent, not live.

  7. Expense structure on a small premium. ¥30,780 of annual premium carries ¥4,000 of maintenance; the five non-benefit lines total ¥120,768.70 against ¥461,030.83 of premium, 26.2%. The 1.0% std inflation rate compounds over 35 years and no Japanese public source supports any of these levels.

Known modeling pitfalls:

  • The projection horizon is not the policy term. T = N + G − 1, not N [S1 第3条第2項] [S3 第3条第3項] [S5] [S12] [S14]. Terminating at t = N on the anchor cell drops ¥2,645.21 of contractual claim outgo, 0.5967% of the total, all of it in months 421–443. It is the most natural error to make and the least visible, because every remaining number still looks reasonable.

  • 最低支払保証期間 is a term extension, not a benefit floor. Both readings pay the same max(N - m + 1, G) instalments, so an undiscounted total cannot distinguish them; they differ in when. A floor implementation compresses the guaranteed instalments inside the term and produces zero cash flow after month 420; the contract pays them after expiry, on the same monthly timetable [S1 第3条第2項]. Test months 421–443 individually, not the total.

  • The in-payment ledger is never decremented. Not by the insured’s mortality, not by the recipient’s, not by lapse [S1] [S5] [S14] [S13 別表1]. Applying the surviving-policy factor (1 − q_m)(1 − w_m) to R(t) — the natural thing to do if R is mistaken for a population of policies — cuts annuity outgo on the anchor cell from ¥443,313.69 to ¥245,605.66, an understatement of 44.6%. This is the largest single error available in this model.

  • Premiums stop on the annuity event; the benefit does not. Premium income carries l(t) and only l(t) [S1 第12条第2項] [S3 第5条] [S8]. Netting premiums against claims on one combined population collects ¥7,535.43 of premium — 1.63% of the total — from policies that are in claim and paying nothing.

  • l(t) and R(t) are disjoint and must never be summed. l(t) is a probability of being in force; R(t) is a count of instalments falling due. They have different units in the model’s economics even though both are dimensionless, and R(420) = 0.016779783 while l(420) = 0.145023 — adding them produces a number with no meaning.

  • The ledger peaks at exactly month N. Every stream opened in months 1 … N − G + 1 ends at month N whenever it opened, so R(N) equals the sum of D(s) over the whole term: 0.016779783 on the anchor cell. An implementation that ends streams at m + n_pay(m) - 1 computed with an off-by-one gets this identity wrong by one month’s claims and nothing else visibly changes.

  • 高度障害 is not a second decrement. 生保標準生命表2018（死亡保険用）includes 高度障害 in its death rate R2 REG-R20, and the two annuities are mutually exclusive [S1 第3条] [S3 第3条] [S5] [S9]. Adding a 高度障害 incidence on top of the table double-counts the benefit.

  • There is no 更新 on this chassis. No retrieved document offers renewal and one states the absence in terms [S5] [S6] [S8]. Importing the chassis’s renewal repricing and d(t) decline invents a decision, a premium ladder and a decrement the contract does not have; the term is 歳満了 only and the premium is level for all N months.

  • Lapse pays nothing. No 解約返戻金 at any duration on the composite [S2] [S5] [S6] [S7] [S9] [S15], so claims_lapse is identically zero. One carrier in the set does write a 低解約返戻金型 design at 70% of the ordinary value [S12] — and on that design, because 保険料払込期間 equals 保険期間, there is no 払込満了 step-up, so the cliff that characterises 低解約返戻金型 whole life has no analogue here. A model importing that cliff invents it.

  • There is no 自動振替貸付. With no cash value there is no collateral, and one carrier states the absence in terms [S2]. The APL mechanic specified in the whole life technical notes (終身保険) must not be imported; the supervisory guideline in any case requires an APL, where one exists, to run at the policyholder’s election rather than automatically REG-R14.

  • A full commutation settles the claim; it does not alter the policy. Paying the whole present value extinguishes the contract [S1 第5条第2項] [S3 第6条第3項] [S12] [S14], so with the module on, the ledger must not open at all for that claim. A model that pays the lump sum and opens the stream doubles the benefit.

  • The リビング・ニーズ cap binds early here, not late. The payout is the present value of an income stream capped at ¥30,000,000 [S2] [S5] [S7], and on the anchor cell the full 年金現価 at issue is ¥56,352,381.90. The cap therefore bites from month 1 and stops biting only once the unpaid stream falls below it — the opposite pattern to a level sum assured, where a cap either always binds or never does.

  • Read the table at the right age, and only on the death basis. 契約年齢 is 満年齢 [S1 第37条] [S14] while 標準生命表2018 is built for 保険年齢 R2 REG-R20, so the base run reads early and understates; the optional shift must move q up. And the 年金開始後用 table has no role on this product at all, because the composite’s stream is an annuity-certain [S13 別表1].