Technical Notes#

Status: Draft, 2026-08-03 (all cited sources accessed 2026-08-03).

Scope note. These notes specify a reference liability cash-flow projection model for the standardized composite product defined in product-spec.md (same directory). This is not any single insurer’s product. [S#]/[R#] tags refer to the source list in sources.md (numbering carried from _research/term-assurance.md; frozen); [REG-R#] tags refer to the cross-product reference library references/regulatory-and-actuarial-references.md (its own R-numbering; research provenance in _research/regulatory-actuarial.md). std marks standardizations introduced for the reference implementation; unverified marks claims not confirmed against a retrieved document. Parameter values are identical to those in product-spec.md.

Model scope and conventions#

  • Purpose. Project gross best-estimate liability cash flows (premiums, death and terminal illness claims by benefit shape, expenses, commission) for a single-policy model point of guaranteed-premium UK term assurance, in the sense required for a Solvency UK best-estimate projection: probability-weighted future cash-flows, gross of reinsurance R1, covering the cash-flow categories of the PRA cash-flows rule (benefits, expenses, premiums, intermediary payments) R2. Discounting, risk margin and capital layers are out of scope (see Valuation and reserve pointers).

  • Projection frequency. Monthly grid std. Every piece of intra-year contractual structure this product has is monthly — the step-down of the decreasing-shape benefit, the FIB instalments, and the premium itself, which is quoted and collected per month [S5] [S6] [S8] — so the grid is the frequency the contract is written in and no mid-year approximation arises. The assumption tables are quoted annually (mortality by attained age, lapse by policy year) and are converted with q_m = 1 − (1 − q)^(1/12) and w_m = 1 − (1 − w)^(1/12) std, which compound back to the annual rate exactly, so the in-force at every anniversary is identical to an annual-grid projection of the same table (a useful implementation check — see the worked example).

  • Time index. t is 0-based and counts policy months from issue: the issue month is t = 0, the policy year containing month t is t // 12 + 1, and the frame is t = 0 … N − 1 where N = 12n is the number of months and the exclusive end. Month t runs from time t to time t + 1: l(t) is the in-force at its start, start-of-month flows fall at time t and end-of-month flows at time t + 1. Where the notes say “policy year k” they mean the contractual label, i.e. months t = 12(k − 1) … 12k − 1.

  • Timing conventions std. Premiums received at the start of each policy month, in advance, and only from policies still in force at that point; maintenance expenses at the start of each month; death/TI claims paid at the end of the policy month of death; lapses occur at the end of the month, after deaths. Acquisition expenses and initial commission at issue (start of t = 0).

  • Age basis. Age nearest birthday at entry, plus curtate policy year — attained age in month t is x + t // 12 std, advancing on the policy anniversary rather than monthly, which is what an age-nearest-birthday basis means. (The fetched product documents do not state an age basis; UK assured-lives tables are select tables — AM92 has a 2-year select period, TMNL16/TFNL16 a 5-year select period R12 — so the mortality interface must accept select-by-duration rates.)

  • Currency. GBP throughout. Benefits are paid in sterling to UK bank accounts [S1].

  • Model points. Single-policy model points projected on an expected (probability-weighted) basis: survivorship factors multiply per-policy cash flows. No aggregation logic is specified here.

  • Termination. All states terminate at the end of the term: cover expires with no maturity value, no renewal, and no conversion — there is no US-style post-level-term ART tail [S1] [S2] [S6] [S8] R8. The projection horizon is exactly N = 12n months, t = 0 … N − 1.

  • Contract boundary. Premiums are guaranteed, so the insurer has no unilateral repricing right and the Solvency UK contract boundary is the full term R3: all N months of premiums and benefits are inside the boundary. (Reviewable-premium variants — CI riders, out of scope — would require the rules 3.3/3.7 test R3.)

  • Rounding. Intermediate values at full precision; displayed cash flows to pence std.

Model point attributes#

Attribute

Type

Example (anchor cell std)

shape

enum {level, decreasing, fib}

level

issue_age

int (age nearest birthday)

35

sex

enum {M, F}

M

smoker

enum {N, S}

N

term_y (n)

int, years (1–50; decreasing 5–50; FIB 5–40)

25

sum_assured (SA0)

GBP (level/decreasing shapes)

150,000

fib_income (I)

GBP/month (fib shape)

1,000

sched_rate (j)

annual effective (decreasing shape)

0.06 std

joint_first_death

bool (base model: false)

false

indexation

bool (RPI option elected)

false

wop

bool (waiver rider; base model: false)

false

premium_monthly (P_m)

GBP/month

12.00 std

premium_mode

enum {monthly, annual}

monthly

issue_date

date

—

The anchor premium is a pure modeling value: no UK insurer publishes premium rate tables (quote-engine pricing; only the £5/month minimum is public [S5]), so any reference premium basis is constructed, not observed std.

State variables#

Variable

Description

Updated

l(t)

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

monthly recursion

q(t), q_m(t)

Annual mortality rate (incl. TI acceleration) for the policy year containing month t, and its monthly equivalent

annual lookup, monthly conversion

w(t), w_m(t)

Annual lapse rate for that policy year, and its monthly equivalent

annual lookup, monthly conversion

D(t)

Expected deaths/TI claims in month t = l(t) × q_m(t)

monthly

DB(t)

Death benefit payable for deaths in month t (shape-dependent)

monthly (schedule)

idx(t)

Cumulative indexation factor (1 if option not elected/declined)

on anniversaries; level within the policy year

FIBcum(t)

Cumulative expected FIB income streams in payment at start of month t = Σ_{s<t} D(s) (fib shape)

monthly

CF(t)

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

monthly

The FIB in-payment ledger is not decremented by mortality after the claim: the instalments are an annuity-certain to the end of the term regardless of any life [S6] [S8].

Two of these step on the policy anniversary rather than every month, and it matters which: q, w, idx and the expense inflation factor are constant through a policy year, because the mortality table is entered at an attained age that advances on the anniversary, the lapse table is keyed by policy year, and the indexation offer is an anniversary event. Only the benefit schedule B(k) and the FIB ledger move monthly.

Assumption inputs#

Three classes are distinguished explicitly.

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

Input

Value

Basis

Premium P_m

Level, guaranteed for the full term

guarantee [S2] [S6] [S9]; level std

Level benefit

SA0 constant

[S1] [S6]

Decreasing benefit schedule

B(k) amortization formula at rate j (below)

mechanics [S1] [S6] [S8]; j = 6% std

FIB benefit

I/month, in arrears, death to end of term; annuity-certain

[S2] [S6] [S8]

Terminal illness

100% acceleration, two-limb 12-month definition, terms ≥ 2 years

[S1] [S6] [S8] R8 [S2] [S4]

Suicide exclusion

12 months, year-one only

[S1] [S6] [S8]

Grace

60 days from due date; then lapse without value

[S1] [S6]

Surrender/paid-up value

None

[S1] [S6] [S8] R8

Indexation option terms

cover +min(max(RPI,0),10%); premium ×(1 + 1.5×increase), cap 15%; removed after 3 declines

[S1] [S2] [S6] [S7]; composite std

Expiry

Cover ceases at end of term; no renewal/conversion

[S1] [S2] [S6] [S8] R8

(b) Insurer-discretionary current elements#

For guaranteed-premium life-only term assurance this class is nearly empty — a deliberate contrast with cash-value products: there are no bonus rates, no MVRs, no reviewable premiums, and no non-guaranteed charge scales on the composite. The two residual discretionary items:

Input

Snapshot value

Basis

FIB commutation basis

Commuted value = PV of remaining instalments at r_c = 3.0% p.a. std snapshot; base model take-up 0%

discretion (“fairly and reasonably”) [S6] [S8]; rate std (no insurer publishes the basis)

Underwriting exclusions / rated terms

None on the composite cell (standard rates)

case-by-case schedule exclusions exist [S1] [S3]; scope std

Reviewable-premium mechanics (5-yearly reviews on claims experience, reinsurance cost, lapses, expenses, etc.) exist on CI-type covers at two of the three carriers [S6] [S8] and are documented there as a modeling template, but are out of scope here.

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

Mortality. The current UK protection experience tables are the CMI “16” Series — term assurance mortality including terminal illness and accelerated CI, graduated on 2015–2018 experience R10 — with public confirmation of the table names TMNL16/TFNL16 (male/female non-smoker, 5-year select) via their adoption in the IFoA Formulae and Tables 2025 edition R12. However, CMI tables issued after 1 March 2013 are subscriber-only R11, so the full 16-Series set (including smoker/duration variants) cannot be redistributed in an open reference implementation. The reference basis is therefore a std proxy, stated honestly:

Input

Recommended public basis

Basis tags

Best-estimate mortality (incl. TI)

Shape of the public “00” Series temporary assurance tables — TMN00/TMS00 (male non-smoker/smoker), TFN00/TFS00 (female), 1999–2002 experience — scaled by a std adjustment factor (suggested 75%) to proxy improvement to the 16-Series era; AM92 (2-year select, prior Formulae and Tables basis) is the teaching-table alternative

tables R13 R11; AM92 role R12; factor std

Mortality improvement

None in base std. The CMI Mortality Projections Model is the market-standard overlay — CMI_2024 (June 2025, WP201) R14, superseded by CMI_2025 (March 2026, WP211) REG-R30 — but the model is subscriber-restricted; a production basis would be “x% of TMNL16/TFNL16 with CMI_2025 improvements at a chosen long-term rate”, all subscriber inputs

R14 REG-R30 R11

Population fallback

ONS national life tables (single-age qx, freely redistributable under OGL) — heavier than insured experience; use only as a last-resort open base

REG-R32

TI acceleration timing

None modeled: death and TI are one decrement, one benefit. Modelling the acceleration on a monthly grid would need a terminal-illness diagnosis basis separate from the mortality table, which the subscriber-restricted tables do not supply, so the payment stays at the month of the combined decrement std

definition [S1] [S6] [S8]; 16-Series mortality includes TI R10

Suicide-exclusion offset

Year-one claims not reduced for excluded suicides std (immaterial; no incidence data in fetched sources)

clause [S1] [S6] [S8]

Lapse. FCA evidence (2024, pure protection in force): average lapse rate 5% p.a.; highest observed early lapse 23% in policy year 1 (non-advised intermediated sales with 4-year clawback); modest lapse spikes just after the 2-year and 4-year commission clawback periods end R9. A full duration curve is not public, so the reference table is std, anchored to the 5% average and the clawback-spike pattern:

Policy year

1

2

3

4

5

6+

Annual lapse w(t) std

10%

8%

7%

5%

6%

4%

The table is keyed by the contractual policy year; w(t) reads the row for policy year t // 12 + 1, so w(t) = 10% for the twelve months t = 0 … 11. The rate is annual and the projection decrements by w_m(t) = 1 − (1 − w(t))^(1/12) std.

(Year 3 staying elevated after the 2-year clawback period ends, and the year-5 uptick after the 4-year clawback period ends, echo the post-clawback spike pattern R9; levels are standardized calibrations to be replaced with the user’s experience.)

Expenses and commission (all levels std; structure evidence as cited).

Input

Value

Basis

Initial (acquisition) expense

£150 per policy at issue

std

Initial commission

150% of annualized premium, paid upfront at issue

upfront pattern ~96% of commission R9; level std

Commission clawback

On lapse in months 1–48: clawback of (48 − months in force)/48 of initial commission, t + 1 months in force at the end of month t (linear, 4-year) — optional module, base model off

clawback periods 2–4 years R9; formula std

Renewal commission

2.5% of premiums from policy year 2 (t ≥ 12)

std

Maintenance expense

£30 per policy p.a. — a twelfth of it each month — inflating 3% p.a. on each anniversary

std

Claim expense

£250 per death/TI claim

std

Expense inflation

3% p.a. flat

std

Cash flow components and recursions#

Notation (defined once, used throughout)#

Symbol

Meaning

t, k

policy month index, 0-based from issue, t = 0..N−1, N = 12n; the two are the same index and k is written where a benefit schedule is meant

y(t)

policy year containing month t = t // 12 + 1; attained age in month t = x + t // 12 (x = issue age)

P_m, P_a

monthly premium = 12.00 (anchor cell) std; annualized premium = 12 × P_m = 144.00

q(t), q_m(t)

annual mortality (incl. TI) rate for policy year y(t), select-adjusted; monthly rate = 1 − (1 − q)^(1/12) std

w(t), w_m(t)

annual lapse rate for policy year y(t); monthly rate = 1 − (1 − w)^(1/12) std (end-of-month, after deaths) [std order]

l(t)

in-force probability at start of month t; l(0) = 1

D(t)

expected claims in month t = l(t) × q_m(t)

SA0

initial sum assured (level/decreasing)

I

FIB monthly income

j, j_m

decreasing schedule annual rate; j_m = (1+j)^(1/12) − 1

B(k)

decreasing-shape benefit after k months (formula below)

idx(t)

cumulative indexation factor in month t (1 if not indexed); steps on anniversaries

E0, e(t)

initial expense (150); maintenance expense = (30/12) × 1.03^(y(t)−1) per month

c0, c_r

initial commission (1.5 × P_a); renewal commission rate (0.025, from t = 12)

ec

claim expense (250)

CF(t)

net cash flow of month t, insurer perspective (+ inflow, − outflow)

Dimensional check: q, w are per-annum probabilities and q_m, w_m per-month probabilities (all dimensionless); B, SA0 are GBP; I is GBP/month and the grid is monthly, so FIB outgo is one instalment per stream per month and carries no month-count multiplier; all CF components are GBP per month.

Benefit amount by shape#

Level: DB(t) = SA0 × idx(t).

Decreasing [S1] [S6] [S8]:

B(k) = SA0 × [(1+j_m)^N − (1+j_m)^k] / [(1+j_m)^N − 1],   B(0) = SA0, B(N) = 0

The schedule steps down monthly, so the balance is constant through month t and the death benefit is that balance exactly:

DB(t) = B(t)

No mid-year reading is needed. (The whole-year identity (1+j_m)^12 = 1+j gives the anniversary balances in closed form, B(12u) = SA0 × [(1+j)^n − (1+j)^u] / [(1+j)^n − 1], which is the quickest way to check an implementation’s monthly convention against an annual one.) Numeric anchor (SA0 = 150,000, j = 6%, n = 25): B(60) = 150,000 × (1.06^25 − 1.06^5) / (1.06^25 − 1) = 150,000 × (4.291871 − 1.338226) / 3.291871 = £134,588 — the benefit after 5 years. Indexation and the decreasing shape are not combined [std scope] (no fetched insurer offers indexed decreasing cover).

Family income benefit [S2] [S6] [S8]: a death in month k triggers N − k monthly instalments of I, in arrears, ending at month N — an annuity-certain independent of survival. On the monthly grid the instalments are counted one by one: each stream in payment pays exactly one instalment at the end of each month, the month of death included, so

Claims_fib(t) = I × [ D(t) + FIBcum(t) ],   FIBcum(t) = Σ_{s<t} D(s)

and one death in month s generates N − s instalments in all, which is the contractual count with no rounding. (An annual grid has to place the death at mid-year and count six instalments in the year of death and twelve in each later year; that approximation is what the monthly grid removes.)

Optional commutation module std: replace the instalment stream at death with a lump sum CV(k) = I × a(N−k) where a(m) = [1 − (1+r_c)^(−m/12)] / [(1+r_c)^(1/12) − 1] is the m-month annuity-certain factor at the snapshot commutation rate r_c = 3% std (contractually the insurer reduces the sum of remaining instalments “fairly and reasonably” [S6] [S8]). On the monthly grid the factor is taken at the exact death month, k = t. Base model: no commutation.

In-force recursion and processing order#

Monthly processing for month t = 0..N−1 std:

  1. Start of month: premium income P_m × idx_p(t) × l(t) (where idx_p(t) is the cumulative premium indexation factor — equal to 1 in the base run), or 12 × P_m × idx_p(t) × l(t) in the first month of each policy year on an annual-mode payer and nil in its other eleven; maintenance expense e(t) × l(t); renewal commission c_r × P_m × idx_p(t) × l(t) (from t ≥ 12). At t = 0 additionally E0 and c0 (per policy issued, l(0) = 1).

  2. Benefit schedule: compute DB(t) per shape (the month’s exact balance B(t) for decreasing).

  3. End of month — claims: expected death/TI outgo DB(t) × D(t) (level/ decreasing) or the FIB formula above; claim expense ec × D(t).

  4. End of month — lapses: applied to survivors of mortality [std order: death before lapse]; lapse pays nothing (no surrender value [S6] R8).

  5. Update:

    l(t+1) = l(t) × (1 − q_m(t)) × (1 − w_m(t))

  6. Anniversary (if indexation elected): at each month t with t mod 12 = 0 and t > 0, with acceptance (behavior section), idx(t) = idx(t−1) × (1 + min(max(RPI, 0), 0.10)) and idx_p(t) = idx_p(t−1) × (1 + min(1.5 × increase, 0.15)) [S1] [S2] [S6]; both are held level through the other eleven months of the policy year.

At the end of t = N − 1 the projection ends: no maturity payment, no tail states [S1] [S6] [S8] R8.

Because q_m and w_m compound back to q and w exactly over the twelve months of a policy year, and because both are constant within the year, the recursion reproduces l(12y) = Π_{u<y} (1 − q(u))(1 − w(u)) — the in-force an annual-grid projection of the same table would report at every anniversary. That identity is the cheapest check on a monthly implementation, and it holds whatever the decrement levels are.

Net cash flow#

Level/decreasing shapes:

CF(t) = P_m × idx_p(t) × l(t)                                   (premiums)
      − DB(t) × D(t)                                            (death/TI claims)
      − ec × D(t)                                               (claim expense)
      − e(t) × l(t)                                             (maintenance)
      − c_r × P_m × idx_p(t) × l(t) × 1{t ≥ 12}                 (renewal commission)
      − (E0 + c0) × 1{t = 0}                                    (acquisition)

FIB shape: replace the claims term with Claims_fib(t) and add − ec × D(t) only in the month of death. Premiums stop at death, but FIB instalments continue — premium income always carries l(t), never the FIB ledger.

What the monthly grid settles. An annual grid has to take the decreasing benefit at the mid-year balance B(12t + 6) and to collect a full year’s premium in advance from lives that may leave during the year; the first understates claims slightly and the second overstates income slightly, and the two are an offsetting pair whose net effect no annual projection can report. Here neither arises: the benefit is the balance of the month the claim falls in and the premium is collected month by month from the lives still in force. An implementation must not carry a further half-year premium adjustment on top — there is nothing left to adjust for.

Waiver of premium (optional module, base off)#

With wop = true, an incapacity state is added: incidence inc(t) std (no public UK incidence basis for the WOP work-tasks definitions is in the fetched sources), 26-week deferred period [S1], premiums waived while incapacitated (premium income multiplied by the active-payer probability), mortality unchanged. The WOP extra premium and the incidence/recovery basis are both std placeholders.

On the monthly grid the deferred period is carried explicitly, as defer = 6 months std — the reading of 26 weeks a monthly grid can express, where an annual one could only round it to “incidence in year t, waiver from year t + 1”. With monthly incidence and recovery rates inc_m, rec_m converted as above, the waived fraction follows

u(t+1) = u(t)(1 − rec_m) + inc_m × [1 − u(t − defer)] × (1 − rec_m)^defer

— the lives entering waiver this month are those who became incapacitated defer months ago and have not recovered since.

Policyholder behavior modeling#

All dynamic formulas are std reference constructions; calibration evidence is cited where it exists.

  • Base lapse std. Duration table above, anchored to the FCA 5% in-force average and clawback-spike pattern R9. Channel matters: the 23% year-1 observation is specific to non-advised intermediated business with 4-year clawback R9; the composite table is channel-blended.

  • Selective lapsation std (optional module). Lapsers are healthier on average; persisters’ mortality is loaded:

    q_eff(t) = q(t) × [1 + λ × max(0, w_cum(t) − w_ref)]

    with w_cum(t) = cumulative lapse proportion to date, w_ref = 0.20 and λ = 0.25 std. Base run: off (λ = 0).

  • Rebroking/dynamic lapse std. Guaranteed premiums mean no premium-shock lapse; the economic driver is rebroking when quoted market premiums for the attained age fall below the in-force premium (younger select lives, falling mortality). A reference multiplier:

    M_reb(t) = min(2.0, max(1.0, P_inforce / P_market(t)))

    applied to w(t), with P_market(t) an external input; base run P_market = P_inforce, so M_reb = 1.

  • Indexation take-up std. If indexation = true: each anniversary the increase is accepted with probability 80% std; after 3 consecutive declines the option is removed [S1] [S6] (two at one insurer [S8]). Deterministic base run: always accept, RPI scenario input flat 3% std, giving a factor of 1.03 on cover and 1.045 on premium at each anniversary (premium factor 1.5 [S1] [S2] [S6]), both held level through the twelve months of the policy year that follows.

  • GIO exercise. Not modeled: exercises create new policies at then-current rates [S1] [S6] [S8], so they add model points rather than changing this one [std scope].

Worked example#

Anchor cell: male 35 non-smoker, single life, level shape, n = 25 (N = 300 months), SA0 = £150,000, P_m = £12.00 std, monthly premium mode; no indexation, no WOP, no commutation; base lapse table; no selective-lapse or rebroking modules. Mortality placeholders q = 0.00055, 0.00060, 0.00065 for policy years 1, 2 and 3 are std illustrative values in the shape of a non-smoker temporary assurance table — they are NOT taken from any CMI table (the current tables are subscriber-only R11; see assumption class (c)). Expenses per the std table: E0 = 150, c0 = 1.5 × 144 = 216.00, e(t) = (30/12) × 1.03^(y−1) per month, c_r = 2.5% from t = 12, ec = 250. Rows are labelled by the 0-based month t; policy year y = t // 12 + 1.

The monthly decrements the first two policy years run on:

Policy year

q

q_m = 1 − (1 − q)^(1/12)

w

w_m = 1 − (1 − w)^(1/12)

1

0.00055

0.00004584

0.10

0.00874161

2

0.00060

0.00005001

0.08

0.00692438

t

y

l(t)

Premiums P_m·l(t)

Claims SA0·D(t)

Claim exp ec·D(t)

Maint. + initial exp

Commission

Net CF(t)

0

1

1.000000

12.00

6.88

0.0115

152.50

216.00

−363.39

1

1

0.991213

11.89

6.82

0.0114

2.48

0.00

+2.59

11

1

0.907479

10.89

6.24

0.0104

2.27

0.00

+2.37

12

2

0.899505

10.79

6.75

0.0112

2.32

0.27

+1.45

24

3

0.827048

9.92

6.72

0.0112

2.19

0.25

+0.75

Trace, t = 0 (first month of policy year 1): D(0) = 1.0 × 0.00004584 = 0.00004584; claims = 150,000 × 0.00004584 = 6.88; claim expense = 250 × 0.00004584 = 0.0115; expenses = E0 + e(0) = 150.00 + 30/12 = 152.50; commission = c0 = 216.00; CF(0) = 12.00 − 6.88 − 0.0115 − 152.50 − 216.00 = −363.39. Update: l(1) = 1.0 × (1 − 0.00004584) × (1 − 0.00874161) = 0.991213.

Trace, t = 12 (first month of policy year 2): premiums = 12.00 × 0.899505 = 10.79; D(12) = 0.899505 × 0.00005001 = 0.00004499; claims = 150,000 × 0.00004499 = 6.75; claim expense = 0.0112; maintenance = (30/12) × 1.03 × 0.899505 = 2.32; renewal commission = 0.025 × 10.79 = 0.27; CF(12) = 10.79 − 6.75 − 0.0112 − 2.32 − 0.27 = +1.45.

The anniversary check. l(12) = 0.899505 and l(24) = 0.827048 are exactly the in-force an annual-grid projection of the same table reports at the first and second anniversaries — 1 × (1 − 0.00055)(1 − 0.10) and that times (1 − 0.00060)(1 − 0.08) — because (1 − q_m)^12 = 1 − q and (1 − w_m)^12 = 1 − w and both rates are constant within the policy year. An implementation whose anniversary in-force drifts from those figures has the decrement conversion wrong.

Totalled over the policy year, the cash flows are:

Policy year

Premiums

Claims

Claim exp

Expenses

Commission

Net CF

1

137.24

78.65

0.13

178.59

216.00

−336.13

2

124.67

77.94

0.13

26.75

3.12

+16.73

3

115.19

78.02

0.13

25.46

2.88

+8.70

Premium income is below the annual grid’s P_a × l(t) in every year — 137.24 against 144.00 in year 1 — and that difference is the annual-in-advance bias, now removed rather than offset: the monthly grid stops collecting from a policy the month it leaves.

The pattern is characteristic of guaranteed term: a deep new-business strain in the first month, t = 0 (upfront commission and acquisition expense against one month’s premium R9) and thin positive margins thereafter — the level premium prefunds the rising mortality cost, so early-duration lapses forfeit margin to the insurer while late-duration lapses relieve it.

Valuation and reserve pointers#

This library projects gross best-estimate liability cash flows; valuation layers consume them and are cited, not reproduced:

  • Solvency UK best estimate. BEL = probability-weighted average of future cash-flows, discounted at the relevant risk-free term structure, realistic assumptions, gross of reinsurance (recoverables separate) R1; required cash-flow categories per the PRA cash-flows rule — benefits, expenses, premiums, intermediary payments, policyholder-charged taxation R2; contract boundary = full term for guaranteed premiums R3. BEL = Σ_t v(t) × [outgo(t) − income(t)] over the recursion above. Note: for profitable guaranteed term assurance the BEL is commonly negative at issue (PV premiums > PV claims + expenses) — an asset on the regulatory balance sheet; models must not floor it at zero (derivation, no source).

  • Risk margin. Technical provisions = best estimate + risk margin REG-R1; cost-of-capital method at 4% with life risk-tapering factor λ = 0.9, floor 0.25 REG-R4 — requires an SCR run-off projection, cited-not-specified here.

  • Regime. PS15/24 completed the restatement of Solvency II assimilated law into PRA rules from end-2024 (“Solvency UK”) R5.

  • IFRS 17. UK-adopted IFRS 17 (adopted 16 May 2022, effective 1 January 2023) applies to IFRS reporters REG-R38; the fulfilment-cash-flow engine is the same expected-cash-flow projection; grouping, CSM and risk-adjustment layers are out of scope [mechanics beyond the adoption facts: unverified].

  • Professional standards. Technical actuarial work using this model in scope of UK regulation falls under TAS 100 v2.0 R15 and TAS 200 v2.0 R16.

Key sensitivities and model risks#

Dominant assumptions, in rough order for a protection block:

  1. Mortality basis risk. The reference basis is a std proxy (scaled “00” Series) because the current 16-Series tables are subscriber-only R11 R13; the proxy scaling factor (75% std) is the single largest lever on claims. Production users should substitute subscriber tables (TMNL16/TFNL16 R12 R10) and a CMI projections overlay R14 REG-R30.

  2. Early-duration lapse. With ~96% of commission upfront and 2–4 year clawback R9, year-1–4 lapse rates drive new-business strain recovery; the clawback module changes the sign of the sensitivity inside the clawback window.

  3. Selective lapsation. Guaranteed premiums plus healthy-life rebroking imply persisting lives are progressively impaired; the λ loading materially moves late-duration claims on long terms.

  4. Expense inflation on small premiums. Premiums as low as £5/month [S5] against £30/year maintenance make per-policy expense inflation a solvency-relevant assumption for small-sum-assured blocks.

  5. Shape-specific risks. Decreasing: the schedule rate j is contractual, so the risk is specification error, not experience (mis-implementing the amortization or the monthly convention); FIB: the annuity-certain run-off means claim outgo persists up to N − 1 months after death — omitting the in-payment ledger understates liabilities.

  6. Indexation take-up. The ×1.5 premium factor [S1] [S2] [S6] makes accepted increases premium-margin-accretive if mortality is proportional to cover; selective acceptance (impaired lives accept, healthy decline) reverses the sign std concern; no public take-up data exists in the fetched sources.

Known modeling pitfalls:

  • TI is not an extra benefit. Death and terminal illness are one decrement and one payment [S1] [S6] [S8]; adding a separate TI decrement double-counts claims. The 16-Series mortality tables already include terminal illness R10.

  • FIB instalments are certain, not contingent. Do not decrement the in-payment income by mortality or lapse; only new claims depend on l(t) [S6] [S8]. Paying only the instalment falling in the month of death understates the liability by up to N − 1 months of income.

  • Decreasing-schedule conventions. j_m = (1+j)^(1/12) − 1 std vs a nominal j/12 convention changes B(k) slightly; state the convention and use the B(60) = £134,588 anchor to validate implementations.

  • Decrement conversion. Convert the annual table rates with 1 − (1 − q)^(1/12), not the nominal q/12: twelve months of the latter leave (1 − q/12)^12 > 1 − q, so it understates the decrement — materially on the 10% year-one lapse rate — and it breaks the anniversary identity above, which is the symptom to look for. Keep the annual rate as the quantity the tables are read in and the monthly one as a derived quantity, so the assumption basis is never restated in monthly units.

  • Do not carry annual-grid corrections onto a monthly grid. The mid-year benefit balance for the decreasing shape and the half-year premium adjustment are both corrections for an annual step. On this grid the benefit is the month’s own balance and the premium is collected monthly from the lives still in force, so applying either on top double-counts a correction for a bias that is no longer there.

  • Lapse pays nothing. There is no surrender value [S6] R8; a lapse row in the cash-flow output must be zero-valued (it affects only l(t)), unlike US models with CSV outflows.

  • No tail states. Terminate everything at month N: no renewal, no conversion, no extended coverage [S1] [S2] [S6] [S8] R8. Importing a US-style post-level-term tail materially misstates UK term liabilities.

  • Joint life first death. Model as a single joint decrement q_joint = 1 − (1−q_1)(1−q_2) on one policy std; the policy pays once and ends [S1] [S6]. Separation/replacement options create new policies and are out of scope.

  • Boundary discipline. All guaranteed premiums are inside the contract boundary R3; truncating premium income at an assumed “repricing” point (a Solvency II habit from reviewable business) is wrong for this product.