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 fund. [S#]/[R#] tags refer to the source list in sources.md (numbering carried from _research/with-profits.md); [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. Mechanics anchors: the PPFMs of three proprietary insurers [S1] [S4] [S5]; regulatory codification of the asset-share item list: PRA Surplus Funds Part R8; canonical methodology literature: Needleman & Roff (1995) on asset shares and Hibbert & Turnbull (2003) on guarantee costs, as listed on the IFoA SA2 resources page R13.

Model scope and conventions#

  • Purpose. Project gross best-estimate liability cash flows (premiums in; death, maturity and surrender claims out; expenses; shareholder transfers) for single-policy with-profits model points on the two composite chassis (unitised bond, conventional endowment), with the smoothed-fund (PruFund-style) variation as an alternative crediting module. Reserves are not computed here (see Valuation and reserve pointers).

  • The asset share is a state variable, not a cash flow. Policy cash flows are premiums, claims (paid at smoothed payouts), expenses and shareholder transfers; the asset share [S1] R8 drives claim amounts through the bonus, smoothing and MVR machinery. The estate absorbs payout-vs-asset-share differences [S1] [S5].

  • Projection frequency. Annual std. Rationale: bonus declarations, the governing discretion cycle, are annual [S1] [S4] [S7]; sub-annual mechanics (daily unit pricing [S4], PruFund daily/quarterly smoothing [S9] [S11]) are compressed to annual equivalents in the base model, with the PruFund module noting its native daily/quarterly grid.

  • Timing conventions std. Premiums and partial withdrawals at the start of the policy year (BOY); fund return accrues over the year; proportional charges, bonus declaration, shareholder transfer and mortality charge at end of year (EOY), in the processing order below; claims and decrements at EOY after declaration.

  • Age basis. Age nearest birthday std — no retrieved UK document fixes a model age basis; ANB is chosen for symmetry with the library’s US convention (its traditional use in UK assured-lives tables is unverified; the currently marketed bond quotes its issue-age limit on an age-next-birthday basis [S10]).

  • Currency. GBP. Single-policy model points, projected on an expected (probability-weighted) basis: survivorship factors multiply per-policy cash flows.

  • Specimen-policy convention. Firms compute asset shares for specimen policies or groups, not necessarily per policy [S1] [S4] [S5] R1 COBS 20.2.5R(2); the reference model computes a per-model-point asset share and treats it as the specimen.

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

Model point attributes#

Attribute

Type

Example (anchor cells, product-spec)

chassis

enum {UWP_bond, CWP_endowment, SF_prufund}

UWP_bond

issue_age

int (ANB)

55 (UWP) / 35 (CWP)

sex

enum {M, F}

M

duration_ifo

int, completed policy years at valuation

5

premium_single

currency (UWP bond)

25,000

premium_regular

currency p.a. (CWP: £60/month → 720 p.a.)

720

sum_assured

currency (CWP basic SA)

20,000

term_years

int (CWP; UWP bond whole-of-life → none)

25

units

float (UWP)

25,000

unit_price

currency (UWP Q; £1.0000 at seed)

1.104081

attaching_bonus

currency (CWP G − SA)

—

asset_share_0

currency (in-force cells)

30,000

smoothed_payout_0

currency (S(0) benchmark for the y/y cap)

29,500

guarantee_dates

list of anniversaries (MVR-free)

{10}

mvr_free_wd_rate

% of original premium p.a.

5%

tax_basis

enum {life_net, pension_gross} [S1] REG-R17

life_net

gao_flag / gao_rate

bool / annuity per £1 cash

false / —

mutual_dist_flag

bool (mutual profit distribution variation [S6])

false

State variables#

Variable

Description

Updated

AS(t)

Asset share at end of year t [S1] R8

annual recursion

Q(t)

With-profits unit price (UWP); never decreases

EOY declaration

FV(t)

Unit face value U(t)·Q(t) (UWP)

EOY

G(t)

Guaranteed benefit SA + attaching reversionary bonuses (CWP)

EOY declaration

b(t)

Declared regular bonus rate for year t

EOY, setting rule

S(t)

Smoothed target payout (after y/y cap and corridor)

EOY

FB(t)

Final (terminal) bonus payable on claim in year t

EOY

MVR(t)

Market value reduction on non-guaranteed exits

EOY

CB(t)

Cost of bonus recognized in year t

EOY

ST(t)

Shareholder transfer = CB(t)/9 (90:10)

EOY

SM(t)

Smoothing account balance (within estate)

on exits

CumGC(t)

Cumulative guarantee-charge deductions (for the 2% lifetime cap [S1])

annual

l(t)

In-force probability at end of year t

EOY decrements

Assumption inputs#

Three classes are distinguished explicitly. Class (a) is contractual/guaranteed; class (b) is the insurer’s current discretionary scale (PPFM-governed discretion R2, advised by the With-Profits Actuary R5); class (c) is the modeler’s view of experience.

(a) Contractual / guaranteed elements (cited)#

Input

Value

Basis

Basic sum assured / premium / term (CWP)

£20,000 / £720 p.a. / 25 years

anchor std, product-spec (15)

Bonus hardening

declared regular bonus increases the guaranteed benefit; contractual once added; guaranteed at death/maturity only

[S1] [S8]

Unit-price floor (UWP)

Q(t) ≥ Q(t−1), i.e. b(t) ≥ 0

[S1] [S4]

Guarantee events (UWP)

death; contractual guarantee dates (10th anniversary); face value + FB payable without MVR

[S4] [S5]; date choice std, product-spec (12)

Death benefit factor (UWP)

g_db = 101% of (FV + FB); MVR never on death

101% std, product-spec (11); no-MVR [S5]

MVR-free withdrawals

≤ 5% p.a. of original premium

std, product-spec (13)

MVR contractual bound

MVR ≤ excess of unit value over underlying asset value

R1 COBS 20.2.16R

PruFund smoothing limits (variation)

daily 5.0% / quarterly 10.0% / gap 2.5% (growth funds); contractual defined terms

[S9] [S11]

(b) Insurer-discretionary current elements (snapshot; revisable under PPFM discipline R2 R5)#

Input

Value

Basis

Regular bonus rate b — UWP

2.00% p.a.

std, product-spec (8) — declarations not public in PPFMs

Reversionary bonus rate b_rev — CWP

1.50% p.a. compound

std, product-spec (16)

Bonus change cap

±1.00% p.a. in normal circumstances; floor 0

[S1] [S7]; adoption std, product-spec (20)

Guarantee-fill target θ

80% of projected maturity asset share

std, product-spec (21); philosophy [S1]

Smoothing y/y cap σ

±10%

[S1]; adoption std, product-spec (23)

Target corridor

80%–120% of asset share

[S1] R1; adoption std, product-spec (22)

AMC c_amc (UWP)

1.00% p.a.

std, product-spec (9)

Guarantee/smoothing charge c_g

0.10% p.a. of asset share; lifetime cap: deductions cease once CumGC ≥ 2% × current asset share

cap [S1]; rate and cap mechanics std, product-spec (10)

Interim bonus rate

= last declared regular bonus rate

practice [S1] [S7]; equality std, product-spec (17)

MVR scale

derived each year from the formulas below (no tabulated scale)

[S5] [S6]; derivation std

EGR (smoothed-fund variation)

5.0% p.a.

std, product-spec (25)

Mutual profit distribution (variation)

0 in base

[S6]; base choice std

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

CMI tables issued after 1 March 2013 are subscriber-restricted R10 REG-R22, so no current CMI rates can be reproduced here: the reference basis is a std proxy on the freely redistributable ONS national life tables REG-R32 (population mortality is heavier than insured experience REG-R32). AM92/AF92 (published 1999) remain the canonical assured-lives shape reference REG-R24; their use in historical with-profits work is unverified convention R10.

Input

Recommended basis

Basis tags

Base mortality

60% × ONS National Life Tables (UK, 2021–2023) qx, sex-distinct

proxy std; source REG-R32; shape cross-check AM92 REG-R24

Mortality improvement

CMI_2025 projections model, long-term rate 1.25% p.a. — named, not reproduced (subscriber-restricted)

model existence REG-R30; LTR choice std

Base surrender rate — UWP bond

5% p.a. flat

std

Base lapse rate — CWP endowment

5% yr 1, 4% yr 2, 3% yr 3, 2% yrs 4+

std

Dynamic surrender multipliers

see Policyholder behavior modeling

std

Paid-up conversion (CWP)

excluded from base model; flag for extension

option exists [S4]; exclusion std

Maintenance expense

£30 per policy p.a., inflating 3.0% p.a.

std

Fund return r(t)

5.0% p.a. deterministic base scenario, net of dealing costs [S5]; net of life-fund tax for tax_basis = life_net cells [S1] REG-R17

scenario level std

GAO take-up (legacy flag)

90% when in-the-money by >10%, else 30%

std [unverified — no public experience retrieved]

Deterministic single-scenario projection is the base; the cost of guarantees requires stochastic valuation (see Cash flow components, cost-of-guarantees note).

Cash flow components and recursions#

Notation (defined once, used throughout)#

Symbol

Meaning

t

policy year index (1, 2, …); x = age at entry (ANB)

P(t)

premium received at BOY t

W(t)

partial withdrawals paid at BOY t

E(t)

insurer maintenance expense in year t (£30 × 1.03^(t−1) std)

r(t)

earned fund return in year t (net basis per tax_basis)

c_amc, c_g

AMC 1.00% p.a.; guarantee/smoothing charge 0.10% p.a. std

q(x+t−1)

mortality rate for year t (class (c) basis)

w(t)

surrender/lapse rate for year t (incl. dynamic multipliers)

MC(t)

mortality charge to the asset share in year t [S1]

b(t), b_rev(t)

declared regular / reversionary bonus rate for year t

Q(t), U(t), FV(t)

unit price, units, face value (UWP); FV = U·Q

G(t)

guaranteed benefit (CWP): SA + attaching bonuses

S(t)

smoothed target payout after cap and corridor

FB(t), MVR(t), TB(t)

final bonus, market value reduction, terminal bonus

CB(t), ST(t)

cost of bonus; shareholder transfer = CB/9

θ, κ, σ

guarantee-fill target 0.80; bonus-smoothing speed 0.5; y/y cap 10% std

g_db

UWP death benefit factor 1.01 std

i_sv

CWP surrender-basis discount rate 4.0% std; v_sv = 1/(1+i_sv)

n

CWP term (25); h = UWP bonus-setting horizon (10 years std)

l(t)

in-force probability at end of year t; l(0) = 1

Annual processing order std#

  1. BOY: premium P(t) received; UWP units purchased: U(t) = U(t−1) + α·P(t)/Q(t−1) with allocation α = 100% (product-spec (7)).

  2. BOY: partial withdrawals W(t) paid (MVR applies if outside the MVR-free allowance); asset share reduced pro rata to the pre-MVR policy value [S1].

  3. Fund return r(t) accrues on the asset share balance.

  4. EOY: proportional charges: multiply by (1 − c_amc − c_g); accumulate CumGC; set c_g = 0 once CumGC ≥ 2% × AS(t) [S1 cap; mechanics std].

  5. EOY: regular bonus b(t) declared per the setting rule below; Q(t) = Q(t−1)(1+b(t)) (UWP) or G(t) = G(t−1)(1+b_rev(t)) (CWP); cost of bonus CB(t) computed on pre-declaration values; shareholder transfer ST(t) = CB(t)/9 deducted from the asset share [S5] R8; product-spec (2).

  6. EOY: mortality charge MC(t) = q(x+t−1) · max(0, DB_g(t) − AS_pre(t)) deducted, where DB_g is the guaranteed death benefit (g_db·FV(t) UWP; G(t) CWP) and AS_pre the balance after step 5 [S1 formula: mortality rate × (death benefit − policy value); guaranteed-only DB in the sum at risk std].

  7. EOY: smoothed payout S(t) computed (cap, then corridor); FB/TB/MVR derived.

  8. EOY: claims paid — deaths at q, surrenders at w, maturity at t = n; smoothing account posts (payout − AS(t)) per exiting unit of probability.

  9. Survivorship: l(t) = l(t−1) · (1 − q(x+t−1)) · (1 − w(t)) (maturity year: survivors mature).

Asset share recursion (core)#

AS(t) = [ AS(t−1) + P(t) − W_AS(t) ] · (1 + r(t)) · (1 − c_amc − c_g)
        − ST(t) − MC(t) + M(t)

Component bases (each item as recorded for the retrospective accumulation [S1] [S2] [S4] [S5] [S6] [S7] and codified in PRA Surplus Funds 3.3 R8):

  • Premiums P(t) — accumulated in full; explicit charges are taken via c_amc rather than allocation deductions std (product-spec (7)).

  • W_AS(t) — asset-share reduction for BOY withdrawals, pro rata to the pre-MVR policy value [S1].

  • Investment return r(t) — actual return on the backing asset pool including unrealised gains [S1] [S5] R8; net of dealing costs [S5]; net of life-fund tax for BLAGAB cells, gross for pensions [S1] [S2] REG-R17; asset shares are not credited with return earned on the estate [S1] [S2].

  • Expenses/charges c_amc — percentage-of-asset-share expense charge; observed 1% caps [S1] [S5]; excess actual expenses over charges fall to the estate [S1].

  • Cost of guarantees and smoothing c_g — deduction from credited return [S1] [S4] [S6]; lifetime cap 2% of asset shares [S1].

  • Shareholder transfer ST(t) — charged to asset shares [S5] R8; one-ninth formulation std (product-spec (2)).

  • Mortality charge MC(t) — rate × sum at risk; actual-vs-charged differences accrue to the estate [S1].

  • Miscellaneous surplus / estate distributions M(t) — allocated annually where applicable [S1] [S5] R8; M(t) = 0 in the base model std (product-spec (3)).

Regular bonus setting rule std#

The PPFM principles are: rates set from projections; gradual changes (±1% p.a. normal); keep a substantial proportion of the payout in final-bonus form; full discretion to declare zero [S1] [S7]. The reference parametrization:

  1. Project the asset share to the horizon at the expected net return r_e = r_base − c_amc − c_g std: AS_proj = AS(t) · (1+r_e)^(m) + future premiums accumulated to the horizon at r_e, with m = n − t (CWP) or m = h = 10 (UWP whole-of-life bond).

  2. Supportable rate: the level bonus rate that grows the guarantee to the guarantee-fill target θ = 80% of the projected asset share:

    • UWP: b_supp = [ θ·AS_proj / FV(t) ]^(1/m) − 1

    • CWP: b_supp = [ θ·AS_proj / G(t) ]^(1/m) − 1

  3. Smoothed declaration with the ±1% discipline [S1] [S7]: b(t) = max( 0, b(t−1) + clamp( κ·(b_supp − b(t−1)), −0.01, +0.01 ) ), κ = 0.5 std.

The base projection holds the snapshot rates (2.00% UWP / 1.50% CWP) level; the rule above is the revision module for scenario work.

Smoothed payout, final bonus, terminal bonus#

Raw target = the unsmoothed asset share (payout target 100% of asset share [S5] [S7] [S8] R1). Apply the year-on-year cap, then the corridor:

S_raw(t)  = AS(t)
S_cap(t)  = clamp( S_raw(t), (1−σ)·S(t−1), (1+σ)·S(t−1) )      σ = 10%  [S1]
S(t)      = clamp( S_cap(t), 0.80·AS(t), 1.20·AS(t) )                    [S1][R1]

The corridor implements the 80–120% target range deterministically at model-point level; the ≥90%-of-policies test [S1] R1 is a portfolio property, out of scope for a single-policy model std.

  • UWP final bonus: FB(t) = max(0, S(t) − FV(t)); guarantee-event payout FV(t) + FB(t); death payout g_db · (FV(t) + FB(t)) [S5: no MVR on death].

  • CWP terminal bonus: TB(t) = max(0, S(t) − G(t)); maturity payout G(n) + TB(n); death payout G(t) + interim accrual + FB per the same scale [S1] [S4] [S8].

  • When the guarantee bites (S(t) < FV(t) or S(t) < G(t)), the excess of the guaranteed payout over the asset share is charged to the smoothing/guarantee account within the estate [S1] [S4].

MVR (unitised, non-guaranteed exits)#

MVR(t) = min( max(0, FV(t) − S(t)),  max(0, FV(t) − AS(t)) )
Surrender payout = FV(t) + FB(t) − MVR(t)

The first argument recovers the smoothed-payout shortfall below face value (post-MVR payouts target 100% of asset share, here its smoothed image [S5]); the second is the COBS 20.2.16R bound — the MVR may not exceed the excess of unit value over the underlying asset value R1. Because FB > 0 requires S > FV and MVR > 0 requires S < FV, final bonus and MVR are never simultaneous (the rule observed in one consolidated with-profits fund [S4]; adoption product-spec (24)). MVR-free events: death [S5], guarantee dates [S4] [S5], withdrawals within the 5% allowance std (product-spec (13)).

Cost of bonus and shareholder transfer (90:10 mechanics)#

ST(t) = CB(t) / 9 — one-ninth of the cost of bonus, so that shareholders receive 10% of each 90:10 distribution (product-spec (2); components [S1] [S5] [S8] R1). Measurement of CB std:

  • UWP regular bonus: CB_reg(t) = b(t) · FV(t−1) — the face-value uplift delivered by the declaration.

  • CWP reversionary bonus: CB_reg(t) = ΔG(t) · v_sv^(n−t) with ΔG(t) = G(t) − G(t−1) — the declared addition discounted to the declaration date (survivorship discount omitted std simplification).

  • Final/terminal bonus: CB_fb(t) = (FB or TB paid on claims in year t), recognized at payment.

ST is a cash outflow from the fund (distribution to shareholders), reported separately in the model output; per COBS 20.2.17AR, adjustments reducing policyholder distributions below the required percentage require proportionate shareholder-transfer reductions R1 — modeled implicitly by tying ST to actually-declared/paid bonus.

Smoothing account#

On each exit, post the smoothing cost (payout − AS(t)) weighted by the exiting probability to SM(t) (within the estate). Intended broadly neutral over time [S1] [S2] [S5] [S6]; the base model tracks the balance without recycling. Optional module: year-end recycling into credited returns as one insurer operates it (maximum deduction currently 2.5% of asset shares p.a.) [S5].

Cost of guarantees — cited, not specified#

The deterministic charge c_g is a charging proxy, not a valuation. The economic cost of the guarantees (unit-price floor, guarantee-date face value, CWP sum assured plus hardened bonuses, GAO) requires stochastic market-consistent valuation: PRA Technical Provisions 9.2 requires guarantees and options to be valued with realistic dynamic assumptions R7, and the canonical methodology is market-consistent stochastic simulation of the bonus/smoothing/MVR rules (Hibbert & Turnbull 2003; Hare et al. 2000 R13). This model produces the per-scenario cash flows such a valuation consumes; the stochastic layer itself is out of scope.

GAO module (legacy flag)#

Where gao_flag is set (CWP pension cells), the retirement benefit is max( CashFund(T) · OMR(T), CashFund(T) · gao_rate ) — the guaranteed annuity rate floors the open-market conversion. GAOs are present in several closed funds, backed by fixed-interest assets, with interest-rate risk identified as a fund business risk [S4]; the 2000 GAO litigation history is unverified context. gao_rate = £0.09 p.a. per £1 of cash fund std [unverified as typical]; take-up per class (c). The GAO is a valuation-critical option (stochastic interest-rate exposure) — cited, not fully specified.

Cash flow outputs (per policy year t, probability-weighted by l)#

Output

Formula

Premium income

P(t) · l(t−1)

Death claims

q(x+t−1) · l(t−1) · DeathPayout(t)

Surrender claims

w(t) · l(t−1) · (1 − q) · SurrenderPayout(t)

Maturity claims

l(n) · (G(n) + TB(n)) (CWP, year n)

Partial withdrawals

W(t) · l(t−1)

Maintenance expenses

E(t) · l(t−1)

Shareholder transfers

ST(t) · l(t−1) plus CB_fb/9 on claims

Policyholder behavior modeling#

All dynamic formulas are std — no public UK with-profits lapse experience was retrieved; the shapes are rationalized from the product’s incentive structure, and dynamic option-exercise modeling is a regulatory expectation for the BEL R7.

  • Base surrender: UWP bond 5% p.a. flat; CWP 5%/4%/3%/2%+ (class (c) table).

  • MVR deterrent: w(t) = w_base(t) · 0.6 while MVR(t) > 0 std — an active MVR penalizes exit, and firms may consider exit volumes in setting MVRs within the COBS bound R1 COBS 20.2.16AR.

  • Guarantee-date spike: w(t) = w_base(t) · 2.5 in a guarantee-date year std — MVR-free encashment is rationally exercised when FV(t) > AS(t) (guarantee in the money); apply the multiplier only in that state.

  • Guarantee-imminent suppression: w(t) = w_base(t) · 0.8 in the year before a guarantee date std (waiting for the MVR-free window).

  • Withdrawal utilisation: withdrawing bond cells take the full 5% MVR-free/tax-deferred allowance; utilisation 30% of policies std (allowance context [S10] REG-R15).

  • GAO take-up: 90% when in-the-money by >10%, else 30% std unverified.

  • Paid-up conversion (CWP): excluded from base std; where modeled, benefits reduce per policy terms and future bonuses may or may not accrue [S4], and asset shares may need separate treatment for altered policies [S6].

Worked example#

Anchor UWP bond cell (product-spec (14)): £25,000 single premium; U = 25,000 units at Q(0) = £1.0000; five declarations at 2.00% give Q(5) = 1.02^5 = 1.104081, FV(5) = £27,602.02. Worked-example state std: AS(5) = £30,000.00, S(5) = £29,500.00. Year-6 parameters: c_amc = 1.00%, c_g = 0.10%, q(60) = 0.005 (illustrative of the class (c) proxy std), g_db = 1.01, σ = 10%. No premium, no withdrawals in year 6. Two return scenarios std: A: r = +7.0%; B: r = −15.0% (declared bonus cut to 1.00%, the maximum normal reduction [S1] [S7]).

Step

Quantity

Scenario A (r = +7.0%)

Scenario B (r = −15.0%)

0

AS(5) / FV(5)

30,000.00 / 27,602.02

30,000.00 / 27,602.02

3

After fund return: 30,000 · (1+r)

32,100.00

25,500.00

4

After charges × (1 − 0.011)

31,746.90

25,219.50

5

Declared bonus b(6)

2.00%

1.00%

5

Q(6); FV(6) = 25,000 · Q(6)

1.126162; 28,154.06

1.115122; 27,878.04

5

Cost of bonus CB = b(6) · FV(5)

552.04

276.02

5

Shareholder transfer ST = CB/9

61.34

30.67

5

Asset share after ST

31,685.56

25,188.83

6

MC = q · max(0, 1.01·FV(6) − AS)

0.00

0.005 × 2,967.99 = 14.84

6

AS(6)

31,685.56

25,173.99

7

S_cap: clamp(AS, 0.9·29,500, 1.1·29,500)

31,685.56 (within)

26,550.00 (floor binds)

7

S(6): corridor clamp to [0.8, 1.2]·AS

31,685.56

26,550.00 (within corridor)

7

Final bonus FB = max(0, S − FV)

3,531.50

0.00

7

MVR = min(max(0, FV−S), max(0, FV−AS))

0.00

min(1,328.04, 2,704.05) = 1,328.04

8

Guarantee-date payout FV + FB (no MVR)

31,685.56

27,878.04 (guarantee bites)

8

Surrender payout FV + FB − MVR

31,685.56

26,550.00

8

Death payout 1.01 · (FV + FB)

32,002.42

28,156.82

8

Smoothing/guarantee cost on exit (payout − AS): guarantee-date / surrender

0.00 / 0.00

2,704.05 / 1,376.01

Checks: scenario B surrender pays exactly the smoothed target (−10.0% y/y, the [S1] cap); the MVR (1,328.04) is below the COBS bound FV − AS = 2,704.05 R1; the guarantee-date exit pays full face value with the 2,704.05 excess over asset share borne by the estate’s guarantee/smoothing account [S1] [S4]. On the scenario A guarantee-date claim an additional shareholder transfer of FB/9 = 392.39 accrues at payment (90:10 on the final bonus, ST section). Scenario A pays 100.0% of AS(6); scenario B’s surrender pays 105.5% of AS(6) — both within the 80–120% corridor [S1] R1.

CWP maturity illustration (one line): at n = 25, G(25) = 20,000 · 1.015^25 = £29,018.91; with smoothed maturity target S(25) = £34,000.00 std, TB = 34,000.00 − 29,018.91 = £4,981.09 — 14.7% of the payout in non-guaranteed form, consistent with the substantial-final-bonus philosophy [S1]; the associated shareholder transfer at payment is TB/9 = £553.45 std measurement.

Valuation and reserve pointers#

This library projects gross best-estimate liability cash flows; valuation layers are cited, not reproduced.

  • Solvency UK BEL. Technical provisions = best estimate + risk margin; the best estimate is the probability-weighted, discounted value of all cash flows R7 REG-R1. For with-profits, the BEL includes future discretionary benefits — future regular and final bonuses expected under PPFM-consistent discretion — because expected payments count “whether or not … contractually guaranteed”, with the surplus-funds carve-out for the unallocated estate R7 R8. The With-Profits Actuary must advise whether the FDB assumptions are consistent with the PPFM R5. Guarantees and options (unit-price floors, guarantee dates, GAOs) must be valued market-consistently with dynamic policyholder behavior R7 — stochastic-on-deterministic use of this model.

  • Risk margin. Post-reform cost-of-capital method: CoC 4%, risk taper λ = 0.9 (floor 0.25) for long-term business R7 REG-R4. Cited-not-specified.

  • Ring-fencing and estate. With-profits fund assets must cover the fund’s liabilities R6; surplus funds (the estate) are own funds, excluded from technical provisions R8. TMTP may apply to pre-2016 back-books R7 REG-R3.

  • Matching adjustment. The guaranteed element of a with-profits immediate or deferred annuity can qualify as an MA “eligible element” REG-R2 — relevant only to the annuity variations, not the composite cells.

  • IFRS 17. UK-adopted IFRS 17 (effective 1 January 2023) applies to IFRS-reporting insurers REG-R38; with-profits contracts are direct-participation business measured under the variable fee approach [unverified — standard text not fetched]. The fulfilment-cash-flow engine is this same projection.

  • Conduct overlay. Payout machinery in any valuation must respect the COBS target-range, MVR-bound and required-percentage rules R1 — they are constraints on the FDB discretion, not just conduct background.

Key sensitivities and model risks#

  1. Fund return / equity backing. Asset shares, final bonuses and MVR incidence all key off r(t); the observed strategy ceiling is a benchmark equity backing ratio of 75% (one insurer’s EBR upper limit [S5]). Deterministic base runs materially understate guarantee costs (convexity) — the central model risk here R7 R13.

  2. Bonus discretion path. The split of payout between hardened regular bonus and final bonus changes guarantee costs without changing the target payout: a higher θ or faster κ hardens guarantees. The std parametrization is a genuine modeling choice with no public calibration.

  3. Smoothing parameters. The ±10% cap and 80–120% corridor determine how much of a market shock passes to payouts immediately; firms’ actual limits vary (5%–15% observed [S1] [S5] [S7]) and can be suspended under solvency stress [S5].

  4. MVR application. Whether the discretion is exercised promptly (and the review buffer — one consolidator tolerates up to 10% return variation before an extra MVR review [S4]) drives surrender strain in down markets.

  5. Surrender behavior at guarantee dates. The guarantee-date spike multiplier and MVR deterrent are unverified std shapes; anti-selective exit when guarantees are in the money is the dominant behavioral risk (dynamic assumptions required R7).

  6. Mortality proxy. The 60%-of-ONS basis is a placeholder; insured with-profits experience differs by class and era, and current CMI tables are subscriber-restricted R10 REG-R22 REG-R32.

  7. Expense and charge caps. Where actual expenses exceed capped charges (1% caps [S1] [S5]) the excess falls to the estate — a fund-level, not policy-level, cash flow this single-policy model does not capture.

  8. GAO interest-rate exposure. Legacy GAO cells are long interest-rate optionality [S4]; omitting the stochastic layer understates their cost materially.

  9. Estate interactions. Reattributions, special bonuses and mutual profit distributions [S5] [S6] are fund-level discretions outside the base model; scenario overlays should treat them as management actions.

  10. Data-provenance limits. Snapshot bonus rates, EGRs and MVR scales are std placeholders by design (declarations are not in PPFMs — research gap); a calibration pass against current bonus declarations is required before any quantitative use.