Technical Notes#

Status: Draft, 2026-08-04 (all cited sources accessed 2026-08-04).

Scope note. A reference liability cash-flow projection model for the standardized composite product defined in product-spec.md (same directory); not any single insurer’s product. [S#] / [R#] tags refer to _research/fixed-indexed-annuity.md; [REG-R#] tags refer to references/regulatory-and-actuarial-references.md, whose shared numbering now runs R1–R157 with most of the R73–R149 block unused: R1–R34 originate in _research/regulatory-actuarial.md, R35–R72 in _research/regulatory-actuarial-annuities.md, and R151–R157 are the seven AP&P Manual appendix items read at first hand on 2026-08-06 — R151 AG 33, R152 AG 35, R153 A-820 with A-821 and A-822, R154 A-830, R155 A-585, R156 A-250, R157 A-255. std marks standardizations introduced for the reference implementation; unverified marks claims the research file could not confirm. An unverified flag leaves that state only when the primary text is read — which is what closed the AG 33 and AG 35 mechanics below REG-R151 REG-R152; nothing is upgraded on recollection, and every flag not closed that way still stands. Parameter values are identical to product-spec.md.

Inherited versus new. The base contract is the fixed deferred annuity chassis in _research/fixed-deferred-annuity.md and products/fixed_deferred_annuity/ — the surrender-benefit composition order and the Model #805 floor construction — whose structure is referenced, not restated; the schedules, rates and recursions below are this composite’s own and are not that file’s. In particular the account-value roll-forward here is index-credit driven, and the lapse architecture below is not that file’s renewal/shock-lapse architecture (see “Policyholder behavior modeling”: an in-force GLWB suppresses the shock lapse). MGV below is the same Model #805 floor that file calls MGSV — one quantity, two source labels. Two base-contract items are restated rather than inherited, because the FIA composite chooses differently from the fixed-deferred composite: the MVA (ratio form [(1+i₀)/(1+iₜ)]^(n/12) − 1 with the specimen limit [S10], against that file’s linear (i₀ − iₜ) × T with a symmetric surrender-charge cap) and the death benefit (max(AV, MGV) [S1] [S2] [S5] [S10], against that file’s full account value floored at the cash surrender benefit). New here: the index crediting engine, the premium bonus with vesting and clawback, and the GLWB rider (benefit base, rider charge, lifetime withdrawal, excess-withdrawal adjustment, post-depletion phase).

Difference from the indexed UL segment engine (products/indexed_ul/technical-notes.md): the FIA shares the vocabulary of segments, caps, participation rates, floors and credit bases, but has no cost of insurance, no net amount at risk and no death benefit corridor, hence no COI/NAAR/corridor circularity. There is no premium load, no per-unit charge and no face amount. The ladder is a single annual segment per indexed account, not a monthly sweep ladder of up to twelve concurrent segments. The rider is a guaranteed lifetime withdrawal benefit that survives account-value exhaustion and pays for life, not a no-lapse guarantee on a death benefit.

Model scope and conventions#

  • Purpose. Project gross liability cash flows (premium, guaranteed and excess withdrawals, surrender payments, death benefits, expenses, and the post-depletion guaranteed income stream) for a single-contract model point. Reserves are not computed.

  • Projection frequency std: monthly, on contract months — with the contract anniversary still the single event date. A monthly grid is not a monthly product. Every contractual mechanic of the composite is annual — annual point-to-point crediting [S2] [S4] [S10], the rider charge at the end of each contract year [S9], the benefit base update [S9], and the lifetime withdrawal — and the model keeps all of them on the anniversary. What the finer grid adds is everything that is not contractually annual: mortality and surrender falling in the month they happen, the fixed account and the Model #805 floor accruing month by month so a mid-year death or surrender is valued on the balance it actually has, and maintenance expense accruing where it is incurred. The excluded variants stay excluded — monthly-sum crediting [S4] R1, one carrier’s monthly charge deduction [S1] [S2], daily interim values [S10] [S11], mid-year withdrawal crediting [S3] [S10] [S11] — and the indexed account is deliberately flat between anniversaries. An annual step remains a special case of the recursions below and reproduces every anniversary value exactly — see Annual equivalence — but it is not what the reference model runs.

  • Time index. t is 0-based and counts contract months, as in MYGA_US_S and lifelib’s basiclife/BasicTerm_S. t = 0 is the first month of a contract projected from issue and the frame is t = 0 … proj_len − 1 with proj_len = 12 × policy_term. Because every contractual schedule is annual, the contract year is derived and used as a lookup key: dur(t) = t // 12 is the completed contract years at the start of month t and the contractual contract year is the 1-based label dur(t) + 1; where these notes say “contract year k” as contract language, the months are t = 12(k − 1) … 12k − 1, and the anniversary month that closes contract year k — where all eight processing steps happen — is t = 12k − 1. Nothing is indexed by the contract year. There is no issue-instant row: the single premium, the bonus and the acquisition expense are beginning-of-month flows of month 0. A contract entered in force after k completed contract years opens at t = 12k, always on an anniversary. State variables are closing values, X(t) being the value at the end of month t; X⁽⁰⁾(t) denotes the value opening the contract year of month t, which is X(12·dur(t) − 1) — the value at the previous anniversary, not at the previous month — or the initialisation value in the first projected contract year.

  • Timing. All transactions occur at the anniversary and are processed as the last events of the contract year ending there std — that is, in the month t = 12k − 1 that closes contract year k. The contract-year surrender charge percentage, vesting percentage and free withdrawal amount therefore all apply to that withdrawal, and the index credit for the year is computed on the balance carried in at the opening anniversary — reproducing the rule that “withdrawals are not credited with index interest in the year they are taken” [S1]. What moves in the eleven other months of a contract year is the fixed-account accrual at (1 + i_F)^(1/12) − 1, the nonforfeiture roll at (1 + i_nf)^(1/12), the decrements at their monthly rates, and one twelfth of the maintenance expense.

  • Age basis: age nearest birthday (ANB) std — the statutory annuity tables are published on that basis (VM-M / Model #821 print the 2012 IAM Period Table for female and male, age nearest birthday) REG-R59, and the AP&P print of the same table at A-821 Appendices I–IV independently carries the “Age Nearest Birthday” heading for both sexes REG-R153. The std stands: it marks the model’s choice of a single age basis, not the tables’ basis. Attained age is issue_age + dur(t), so age changes on the anniversary and not on the birthday: the contract year of month t opens at attained age x + dur(t) — the age its annual mortality rate is read at — and its transactions fall one year older, at x + dur(t) + 1.

  • Model points. Single-contract, projected on an expected (probability-weighted) basis; survivorship and persistency factors multiply per-contract cash flows. No aggregation logic specified.

  • Decrement order: death before surrender std. Rounding: full precision internally, cents on reported cash flows std. State basis: one composite state basis std.

Model point attributes#

Attribute

Type

Example (anchor cell)

issue_age

int (ANB)

62 std

sex

enum {M, F}

M

tax_status

enum {NQ, Q}

NQ std

single_premium

currency

100,000 std

bonus_rate

rate

0.07 [S5]

alloc_fixed / alloc_indexed

fraction (sums to 1)

0.00 / 1.00 std

glwb_elected / glwb_basis

bool / enum {single, joint}

true / single std

joint_age

int (ANB), joint only

n/a

income_start_age

int (ANB), ≥ 50 [S2] [S3] [S9]

70 std

utilization_intensity

fraction of LW actually withdrawn

1.00 std

sc_schedule

vector, contract years 1–11+

9.1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 % [S5]

vesting_vector

vector, contract years 1–11+

0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 % [S5]

mva_index_at_issue i₀

rate

0.0300 std

av_initial, bb_initial, mgv_initial

currency (in-force cells)

107,000 / 100,000 / 87,500

State variables#

Variable

Description

Updated

F(t)

Fixed account balance closing month t

monthly — it accrues at (1 + i_F)^(1/12) − 1

A(t)

Indexed account balance closing month t

annually, at the anniversary: the segment credits only at maturity

AV(t)

Account value = F(t) + A(t)

monthly through F; the contractual steps at the anniversary

MGV(t)

Guaranteed minimum (nonforfeiture) value

monthly — accretes at (1 + i_nf)^(1/12), deducts at the anniversary

BB(t)

GLWB benefit base — notional, no cash value [S1] [S9]

annually, at the anniversary

RB(t)

Rollup base for the guaranteed simple rollup [S2] [S9]

annually / on withdrawal

LW(t)

Locked annual lifetime withdrawal amount (0 before exercise)

at exercise; ratchet; excess withdrawals

phase(t)

ACCUM / INCOME / DEPLETED / TERMINATED

annually, at the anniversary

v(t), sc(t)

Vested bonus percentage; surrender charge percentage for the contract year of month t, dur(t) + 1 [S5]

schedule lookup

FW(t)

Free withdrawal amount = 0.10 × AV⁽⁰⁾(t), on the balance opening the contract year

annually

Wcum(t)

Cumulative gross withdrawals

on withdrawal

l(t)

In-force probability at the start of month t; l(0) = 1, and l at month 12k is the probability in force at anniversary k

monthly decrements

rider_in_force(t)

Boolean; false once the rider terminates [S9]

on events

depletion_cause(t)

Flag set when an excess withdrawal, surrender charge or MVA touches the account value

in step 5

Assumption inputs#

Class (a) is contractual and cannot be changed by the insurer; class (b) is the insurer-declared current scale, a non-guaranteed element under ASOP No. 2 R6 REG-R26; class (c) is the modeler’s view of experience. They must not be mixed in the code.

(a) Contractual / guaranteed elements#

Input

Value

Basis

Index credit floor f

0%

[S1] [S4] [S10] R1

Guaranteed minimum annual cap c_min

0.25%

[S4]; selection std

Guaranteed minimum fixed rate i_F,min

1.00%

[S10]; selection std

Surrender charge schedule sc(t)

9.1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0%

[S5]

Surrender charge base

gross withdrawal − free withdrawal amount

[S10]

Free withdrawal

10% of the prior-anniversary account value, no carry-forward

[S1] [S3] [S5] [S6] [S9] [S10]; combination std

Bonus vesting vector v(t)

0, 10, …, 100%

[S5]

Bonus clawback

(1 − A) × [B/(1+B)] × C

[S10]

MGV base / rate i_nf

87.5% of premium excluding the bonus / 1.00% inside the 0.15%–3% corridor

[S10] R2; level std

Guaranteed simple rollup g(t)

5.00% (yrs 1–10), 2.00% (yrs 11–20), 0% after

[S2]

Rollup base convention

flat dollar increment on premium adjusted for withdrawals

[S2] [S9]

Stacking factor m

150% of dollar credits, floored at 0

[S8] [S9]

Growth period T_g

min(first lifetime withdrawal, contract year 20)

[S1] [S2]

Lifetime withdrawal percentages π

age-band table (product-spec.md); joint = single − 0.50%

[S3] [S1]; 80+ band std

Minimum age for lifetime withdrawals

50

[S2] [S3] [S9]

Rider charge maximum

1.50%, changeable only after contract year 15

[S9]

Post-depletion guarantee

income continues if depletion is caused by guaranteed withdrawals or rider charges; terminates if caused by excess withdrawals, surrender charges or MVA

[S1] [S9]

Death benefit ≥ cash surrender benefit

statutory constraint

R2 §6

(b) Insurer-declared current elements (snapshot; revisable NGEs R6 REG-R26)#

Input

Value

Basis

Declared annual cap c

5.25%

[S2] (rates effective 07/01/2022); selection std

Declared fixed account rate i_F

2.30%

[S2]

Rider charge rate φ

0.95% of the benefit base

[S9]

Allocation / strategy charge

0%

current 0%, max 2.50% [S3] [S4]; choice std

MVA reference index level iₜ

scenario input

generic std; Barclay’s US Credit Index in the linear-form products [S6] [S7]

Caveat. Every value here is a non-guaranteed element captured only as of the date on its source document, and one carrier’s current rate sheets could not be fetched [S-f1]. Insurers review caps, participation rates, spreads and triggers frequently (e.g. monthly), targeting the priced product option budget and considering investment yields, option costs, volatility, premium volumes, competition and profit objectives R1. Reference re-declaration rule std: set c(t) so the one-year call-spread cost equals the option budget b_opt(t) = earned_rate(t) − required_spread, subject to c(t) ≥ c_min R1 R6. The base projection holds the snapshot scale level.

(c) Behavioral and experience assumptions#

Input

Recommended public basis

Tags

Annuitant mortality

2012 IAM Basic / 2012 IAR generational with Projection Scale G2: q_x^{2012+n} = q_x^{2012} × (1 − G2_x)^n, rounding applied from the 2012 period rate each time, never by compounding an already-rounded rate

REG-R59 REG-R60

Mortality A/E deviation

2020–2024 Individual Payout Annuity Mortality Experience Study (23 parent groups, >80% of industry sales, 3.1m contract-years, 143,190 deaths), presented against the 2012 IAM Table

REG-R61; A/E factor 100% std

Deferred-period mortality

materially under-evidenced — only a 2011–2015 deferred annuity mortality study and a 2006 analysis are public; qualified contracts show lower A/E than non-qualified, and FIAs without GLWBs showed an anomalous increasing A/E by account-value band

R1 REG-R65

Base surrender

shape: low early, rising through the surrender charge period, spiking in the shock year, then falling back but staying above pre-shock levels

R1; table std

Shock lapse

in the year the surrender charge expires, 10% with a GLWB rider versus 33% without

R8; corroborated unverified at REG-R62

GLWB withdrawal incidence

37% of GLWB contracts took withdrawals in 2019–2020 versus fewer than 30% without

R8

GLWB withdrawal efficiency

the majority of users withdraw 95%–105% of the maximum; contracts in that band have the lowest surrender rates; activated GLWBs lapse least

R1

GLWB activation timing

clusters at the required-minimum-distribution age; withdrawal rates rise with attained age, highest for qualified contracts at 70+

R1; REG-R64 unverified; assumption framework REG-R67

Additional premium

rare: 2.5% of contracts in years 2–10, 1.9% with a GLWB, 3.3% without

R8

Maintenance expense

$80 per contract per year, inflating 2.5% p.a.

std

Acquisition expense

6.0% of single premium at issue

std

Premium tax

0.0% (composite state basis)

std

The Academy’s guaranteed-living-benefit resource guide is the checklist to test a utilization assumption against — moneyness, age and RMD timing, qualified versus non-qualified, distribution channel, systematic withdrawal plan enrolment, rider type — and is explicitly non-binding, “a list of considerations and resources” REG-R67. The detailed FIA surrender and utilization tables are behind paid subscriptions R9 REG-R62, so every class (c) number is an order-of-magnitude anchor, not a calibration target.

Cash flow components and recursions#

Notation (defined once)#

Symbol

Meaning

t

contract month index, t = 0, 1, …, proj_len − 1; dur(t) = t // 12 is the completed contract years and dur(t) + 1 the contractual label

12k − 1

the anniversary month closing contract year k, where all eight processing steps happen; every formula below with an annual step is evaluated there

X⁽⁰⁾(t)

the value opening the contract year of month t for any state X: X(12·dur(t) − 1) — the previous anniversary, not the previous month — or the initialisation value in the first projected contract year

x

issue age (ANB); attained age is x + dur(t), so the contract year of month t opens at x + dur(t) and its transactions fall at x + dur(t) + 1

P, b, v(t)

single premium; bonus rate (0.07 [S5]); vested percentage in year t [S5]

F(t), A(t), AV(t)

fixed / indexed / total account value closing month t, after all processing

I(y), R(t)

index level at anniversary number y — not a month index; R(t) = I(y+1)/I(y) − 1 with y = dur(t), the return over the contract year of month t (price index, dividends excluded [S6] R1)

c, c_min, f

declared cap (0.0525 [S2]); guaranteed minimum cap (0.0025 [S4]); floor (0)

p, s, d, c_m

participation rate; spread / index margin; trigger rate; monthly cap (variants)

cr(t), IC(t)

credit rate and index credit amount for the contract year of month t, both realised in the anniversary month

FI(t), FI_a(t)

fixed account interest for month t; for the whole contract year, F⁽⁰⁾(t) × i_F, which is what the benefit-base stack uses

i_F, i_F,min

declared / guaranteed minimum fixed rate (0.0230 [S2] / 0.0100 [S10])

φ, Φ(t)

rider charge rate (0.0095 [S9]); rider charge amount

BB(t), RB(t), g(t), m

benefit base; rollup base; rollup rate [S2]; stacking factor (1.50 [S8] [S9])

LW(t), π(a, basis)

annual lifetime withdrawal amount; payout percentage at attained age a [S3]

G(t), E(t), ρ(t)

gross withdrawal; excess above LW; proportional reduction factor

FW(t), X(t)

free withdrawal amount = 0.10 × AV⁽⁰⁾(t); chargeable amount

SC(t), CB(t), MVA(t)

surrender charge; non-vested bonus clawback; MVA (signed)

MGV(t), i_nf

guaranteed minimum value; nonforfeiture accumulation rate (0.0100 std)

i₀, iₜ, n

MVA index at issue, at withdrawal; months remaining in the MVA period

q(t), w(t)

annual mortality and surrender rates of the contract year containing month t

q_m(t), w_m(t)

the monthly rates actually applied, 1 − (1 − q)^(1/12) and 1 − (1 − w)^(1/12)

l(t)

in-force probability at the start of month t; l(12k) is the probability in force at anniversary k

Dimensional check. cr is dimensionless, so IC = base × cr is currency; Φ = φ × BB is currency — a rate applied to a notional amount (the benefit base has no cash value [S1] [S9]) producing a real deduction from the account value; LW = π × BB is currency per year; ρ is dimensionless. All account-value terms are currency.

Initialisation (the state opening month 0)#

The premium arrives at the start of the first contract year rather than at an instant of its own, so these are the opening values of month 0, not a row before it:

A⁽⁰⁾(0) = alloc_indexed × P × (1 + b)   F⁽⁰⁾(0) = alloc_fixed × P × (1 + b)  [S5]
AV⁽⁰⁾(0) = P × (1 + b) = 107,000
BB⁽⁰⁾(0) = P = 100,000     RB⁽⁰⁾(0) = P = 100,000                            [S9]
MGV⁽⁰⁾(0) = 0.875 × P = 87,500         (bonus excluded)                      [S10] [R2]
LW⁽⁰⁾(0) = 0   phase⁽⁰⁾(0) = ACCUM   rider_in_force⁽⁰⁾(0) = true   l(0) = 1

A contract entered in force after k completed contract years opens month 12k on stated balances in the same way, always on an anniversary.

Processing order for a contract year, in the anniversary month closing it std#

Fixed for the reference model, following one specimen’s stated sequence — the rider charge is deducted after index credits are added [S9] — with the benefit-base update after the charge, so the charge is always assessed on the opening base as Φ(t) = φ × BB⁽⁰⁾(t).

  1. Index credit and fixed interest. 2. Rider charge. 3. Benefit base: rollup, stack, step-up.

  2. Lifetime / excess withdrawal. 5. Charges on the excess and proportional reduction of the guarantee. 6. Guaranteed minimum value roll. 7. Phase transition (incl. depletion test).

  3. Decrements. Steps 1–3 are skipped in DEPLETED; steps 1–7 in TERMINATED.

Which of the eight run in an ordinary month. Steps 2, 3, 4, 5 and 7 are wholly annual and run only in the anniversary month t = 12k − 1. Step 1 splits: the fixed account accrues every month at (1 + i_F)^(1/12) − 1, while the index credit is earned only at segment maturity, so IC(t) = 0 in every other month and the indexed balance is flat between anniversaries. Step 6 splits the same way: the floor accretes monthly and the withdrawal is deducted at the anniversary. Step 8 runs every month, on q_m and w_m.

Step 1 — index credit.

cr(t) = max( f , min( c , R(t) ) )                              [S2] [S4] [S10] [R1]
IC(t)   = A⁽⁰⁾(t) × cr(t)        at t = 12k − 1, else 0
FI(t)   = F(t−1) × [ (1 + i_F)^(1/12) − 1 ]      every month
FI_a(t) = F⁽⁰⁾(t) × i_F          the contract year's total, for the stack
AV⁽¹⁾(t) = AV(t−1) + IC(t) + FI(t)

The twelve monthly accruals of FI compound to exactly FI_a, because nothing else touches the fixed account between anniversaries, so AV⁽¹⁾ at the anniversary is what an annual step would have produced. The benefit-base stack in step 3 is computed on FI_a, the year’s figure, not on the anniversary month’s own accrual.

Variants, all floored at f: max(f, p × R) [S4] [S10] R1; max(f, min(c, p × R)) — worked at R1 as min(80% × 10%, 6%) = 6%; max(f, p × R − s) [S8] R1; d × 1{R ≥ 0} R1; max(f, Σ_{k=1..12} min(R_k, c_m)) [S4] R1.

Segment bookkeeping. One annual segment per indexed account, created at anniversary t with balance A⁽⁰⁾(t) and maturing at anniversary t + 1; the credit locks at maturity and cannot be lost to later declines [S1]. The credit base is the segment’s opening balance less withdrawals from that account during the segment — the “Interest Credit Basis” [S6] — which collapses to A⁽⁰⁾(t) here because all transactions occur at anniversaries std. Reallocation is permitted at each anniversary [S1] [S5]; dividends are excluded from R(t) [S6] R1. The floor applies to the credit, not to the account value — charges do reduce the account value below its prior balance [S7].

Mid-segment value. The finer grid makes this a live question, because a death or a surrender can now fall inside a segment. The retrieved documents offer four conventions: no credit in the year of withdrawal [S1]; prorated for the portion of the year the money stayed in the allocation [S3]; G × PAR/(1 + PAR), PAR being a Protected Account Return and not a participation rate [S10]; full earnings-to-date on the free amount and pro rata above [S11]. The composite adopts the first and applies it to every mid-year exit std: the indexed balance is flat between anniversaries and a contract leaving mid-year takes no part of the segment with it. That is the one convention stated as a rule rather than as a valuation method, and the other three are interim-value structures the notes exclude. It is also the conservative reading for the holder only in a bad index year, so it is marked rather than assumed.

Step 2 — rider charge.

Φ(t) = φ × BB⁽⁰⁾(t)         AV⁽²⁾(t) = AV⁽¹⁾(t) − Φ(t)                        [S9]

Deducted from the fixed account first, then proportionately across indexed accounts [S9]. φ is fixed for 15 contract years, then resettable but never above 1.50% [S9]. Variants: charge on the contract value [S5]; no explicit charge, the guarantee funded through lower caps, participation rates or higher index margins [S3] [S8]. The composite does not deduct the charge from MGV; one carrier deducts from both the accumulated value and the minimum guaranteed contract value except in certain states [S1] [S2], and another deducts its allocation charge from the guaranteed minimum value in most states [S3] [S4] — implement as a switch std.

Step 3 — benefit base.

rollup(t) = g(t) × RB⁽⁰⁾(t)                   inside T_g, else 0        [S2] [S9]
stack(t)  = m × max( 0 , IC(t) + FI(t) )      inside T_g, else 0        [S8] [S9]
BB⁽³⁾(t)  = BB⁽⁰⁾(t) + rollup(t) + stack(t)
BB⁽⁴⁾(t)  = max( BB⁽³⁾(t) , AV⁽²⁾(t) )              annual step-up **[std]**

T_g = the earlier of the first lifetime withdrawal and contract year 20 — that is, months with dur(t) + 1 ≤ 20 [S1] [S2]. The rollup is a flat dollar increment, not simple interest on the grown base — one carrier computes it on premium less withdrawals [S2], another on the adjusted initial base [S9], and the latter’s 15-year table confirms a constant $3,000 per year on a $100,000 adjusted initial base [S9]. The stack is on realised dollar credits net of any strategy fee, floored at zero [S9].

The step-up is a std generalisation. No retrieved document describes an automatic annual ratchet during deferral; documented instead are an at-exercise step-up to the contract value [S5], an annual benefit amount computed on the greater of base and account value at exercise [S9], and a never-decreasing income amount once withdrawals begin [S3]. Testing once at exercise reproduces [S5]/[S9]; testing annually is the superset. Under the blended baseline the step-up rarely binds — an extra dollar of credit adds $1 to the account value and $1.50 to the base — so it binds mainly in the pure-rollup variant (see the worked example). Rarely, not never: the account-value bonus opens contract year 1 at AV⁽⁰⁾ = 107,000 above BB⁽⁰⁾ = 100,000, so a first contract year with a zero index credit gives AV⁽²⁾ = 106,050 against BB⁽³⁾ = 105,000 at its anniversary, month t = 11, and the step-up binds. Test it at every anniversary rather than assuming the stack dominates.

Three growth mechanisms must be expressible; the baseline is (c):

Mechanism

Configuration

Observed at

(a)

Guaranteed deferral rollup only

m = 0; g simple on RB, or compound on BB

[S1] [S2] simple, [S5] compound (Options 1, 3, 5), [S9] simple

(b)

Index-credit stacking only, no guaranteed rollup

g = 0; m = 1.50 or 2.50

[S3] [S4] (150% or 250%, by annual owner election)

(c)

Blended — baseline std

g = 5.00%/2.00%, m = 1.50

[S2] [S8] [S9]

In design (b) the account value is deliberately starved: one carrier’s 250% election credits 250% of index interest to the benefit base but only 50% to the account value, and the contract defaults to the 150%/100% election once lifetime withdrawals begin [S3]. Model this as an account-value interest factor κ ∈ {0.50, 1.00} applied to IC(t) in step 1, with the benefit-base factor m [S3] [S4]. In the benefit-base-only bonus designs the bonus is added to BB⁽⁰⁾(0) and never touches the account value or the surrender benefit [S3] [S4] [S8].

Step 4 — lifetime and excess withdrawal. Exercise is permitted from attained age 50 [S2] [S3] [S9]:

LW(t) = π( x + t + 1 , basis ) × BB⁽⁴⁾(t)                                [S3] [S9]

π is read at the attained age at the anniversary the withdrawal is taken, x + t + 1, and is locked at first exercise std; joint = single − 0.50% on the younger life [S1] [S3]. After exercise the ratchet still applies — LW(t) = max( LW⁽⁰⁾(t) , π × BB⁽⁴⁾(t) ) — so income never decreases [S3]. For a gross withdrawal G(t):

guaranteed portion = min( G(t) , LW(t) )      E(t) = max( 0 , G(t) − LW(t) )
AV⁽⁵⁾(t) = AV⁽²⁾(t) − G(t)

Withdrawals up to LW carry no surrender charge, no MVA and no bonus clawback even if LW exceeds the free withdrawal amount [S9]; unused LW does not carry forward [S9] (one carrier accumulates it without interest as a “cumulative withdrawal amount” [S3]).

Step 5 — charges on the excess and proportional reduction.

X(t)   = max( 0 , G(t) − FW(t) )                      pre-exercise
X(t)   = max( 0 , E(t) − remaining free withdrawal )  post-exercise **[std]**
SC(t)  = X(t) × sc(t)                                                    [S5] [S10]
CB(t)  = ( 1 − v(t) ) × [ b / (1 + b) ] × X(t)                           [S10]
MVA(t) = X(t) × { [ (1 + i₀) / (1 + iₜ) ]^(n/12) − 1 }                   [S10]

n is the months remaining in the MVA period, n/12 = surr_charge_period − (t + 1)/12, and the monthly grid carries it exactly: at the worked example’s anniversary 8 — month t = 95 — that is 10 − 96/12 = 2 years, the 24 months the source quotes, while a surrender six months earlier now carries the 30 months it actually has rather than being rounded to the anniversary. Every anniversary value is unchanged.

Whether the guaranteed withdrawal consumes the free withdrawal amount is a std choice. [S9] says only that withdrawals up to the annual benefit amount carry no charge “even if greater than the Free Withdrawal Amount”; it does not say whether they exhaust it. The convention above — remaining free withdrawal = max(0, FW(t) − LW(t)) — is the insurer-favourable reading and is what the worked example uses; the alternative leaves the full FW(t) available against the excess.

MVA is signed — negative when the reference yield has risen [S10] — and is limited to |MVA| ≤ max(0, G(t) − SC(t) − CB(t) − MGV(t)), so a negative MVA combined with charges never reduces the surrender value below the guaranteed minimum value and the maximum positive MVA cannot exceed the maximum negative MVA [S10]. MVA = 0 outside the MVA period and on the death benefit [S5] [S6] [S7] [S10].

pre-exercise    ρ(t) = G(t) / AV⁽²⁾(t)                          [S1] [S3] [S5] [S9]
post-exercise   ρ(t) = E(t) / ( AV⁽²⁾(t) − LW(t) )                       [S9]
BB(t) = BB⁽⁴⁾(t) × (1 − ρ)     LW(t) ← LW(t) × (1 − ρ)     RB(t) = RB⁽⁰⁾(t) × (1 − ρ)

with ρ = 0 when E(t) = 0, and ρ = 1 (base to zero, rider terminates [S9]) if the post-exercise denominator is non-positive. The post-exercise denominator is the account value after the guaranteed payment has notionally been taken — verbatim at [S9]: account value $100,000, base $200,000, annual benefit amount $10,000, withdrawal $28,000 → denominator $90,000, excess $18,000, reduction 20%, base → $160,000, benefit amount → $8,000. An RMD above LW is not an excess withdrawal after exercise; before exercise it reduces the base pro rata [S1] [S9]. The alternative rollup-base convention — the dollar subtraction, “Premium minus Withdrawals” [S2] — is RB(t) = max(0, RB⁽⁰⁾(t) − G(t)).

Step 6 — guaranteed minimum value.

MGV(t) = max( 0 , MGV⁽⁰⁾(t) × (1 + i_nf) − G(t) )                        [R2] [S10]

with MGV⁽⁰⁾(0) = 0.875 × P excluding the bonus [S10]. Model #805 §4A also permits an accumulated $50 annual contract charge and accumulated premium tax to be deducted R2; both are set to zero std because no retrieved product declares an actual annual policy fee, making the modeled floor slightly conservative. Contractually i_nf = min(3%, max(0.15%, CMT₅ − 125 bp − Δ)) where Δ ≤ 100 bp is the FIA additional reduction available while the contract provides substantive participation in an equity indexed benefit R2; Δ requires an annualized option cost of the guaranteed index features ≥ 25 bp and then equals min(100 bp, annualized option cost), certified annually R3. Whether the 15 bp floor of §4B(3) survives the §4C reduction is not stated in the retrieved text unverified; the contract language “the interest rates will range between 0.15% and 3%” suggests it does [S10]. Correction: the §4B floor is 15 basis points, not 1% R2; the composite’s 1.00% is a std pick inside the corridor, not the statutory floor.

Step 7 — phase transitions and the post-depletion liability.

ACCUM    → INCOME      first lifetime withdrawal, attained age ≥ 50      [S2] [S3] [S9]
INCOME   → DEPLETED    AV ≤ 0 attributable only to guaranteed withdrawals
                       and rider charges                                 [S1] [S9]
INCOME   → TERMINATED  AV ≤ 0 attributable to an excess withdrawal, a
                       surrender charge or an MVA                        [S1] [S5] [S9]
any      → TERMINATED  death, full surrender, or BB reaching zero        [S9]
DEPLETED → TERMINATED  death of the covered person only                  [S1] [S9]

DEPLETED is where the economic value of the guarantee sits. In it the insurer pays LW annually from its own funds for the rest of the covered life [S1] [S3] [S9] R1; there is no account value, so no rider charge is deducted [S9] and no index credit is computed; the surrender value and death benefit are zero; lapse is impossible, so every surrender and dynamic-lapse formula must be switched off and l(t+1) = l(t) × (1 − q_m(t)); under the joint option the payment continues to the survivor [S1] [S9]. The attribution test is not cosmetic — an account value run to zero by an excess withdrawal loses the guarantee entirely [S1] [S5] [S9]. Implement it as depletion_cause, set in step 5 whenever E(t) > 0, SC(t) > 0 or MVA(t) < 0, and evaluate it before the depletion test. One carrier’s confinement and terminal illness waivers are themselves excess withdrawals that terminate the income rider [S1] — a trap if waivers are added.

Step 8 — decrements and cash flow outputs. The one step that runs every month:

q_m(t) = 1 − (1 − q(t))^(1/12)      w_m(t) = 1 − (1 − w(t))^(1/12)
l(t+1) = l(t) × (1 − q_m(t)) × (1 − w_m(t))

with w(t) = 0 in DEPLETED. The annual rates are properties of the contract year: q is read at x + dur(t) and w at the phase and moneyness closing that year, so both are constant across its twelve months and the conversion is exact rather than an averaging. Every flow of month t is weighted by l(t), the probability in force at the start of that month, because the processing precedes the decrements.

The shock lapse is spread: the notes state it as the surrender rate of contract year 11, a year carrying no surrender charge in any of its months, so there is no contractual date inside it for the decision to cluster on. (Contrast Term_US_S, where the notes put the shock “in full at the end of the final level-period month” and the whole of it lands there.) The one surrender that is not spread is the deemed full surrender at termination, a contractual event: [S5] treats the contract “as well as the rider” as Surrendered on the date the account value is destroyed, so w_m = 1 in that anniversary month and zero before it.

Cash flow

Formula

Weight

Premium income (+)

P at the start of t = 0

1

Guaranteed withdrawal (−)

min(G(t), LW(t)), at t = 12k − 1

l(t)

Excess withdrawal (−)

E(t) − SC(t) − CB(t) + MVA(t), at t = 12k − 1

l(t)

Surrender (−)

CSV(t) = max( AV(t) − SC(t) − CB(t) + MVA(t) , MGV(t) )

l(t) × (1 − q_m(t)) × w_m(t)

Death benefit (−)

max( AV(t) , MGV(t) ), full bonus vesting, no charges

l(t) × q_m(t)

Post-depletion income (−)

LW while phase = DEPLETED, at t = 12k − 1

l(t)

Acquisition expense (−)

6.0% of P at the start of t = 0 std

1

Maintenance expense (−)

(80/12) × 1.025^(t/12) std

l(t)

The withdrawal lines are weighted by the in-force at the anniversary month, l(12k − 1) — the contracts that actually reach the anniversary. That is the one place the finer grid changes an answer rather than its resolution: an annual step could only weight the year’s guaranteed withdrawal by the contracts that entered the year, and so paid a full year of income to a contract that died in month three.

SC, CB and Φ(t) are internal transfers within the account value, not separate cash flows — they reduce what is ultimately payable. Reporting them as fee income while also projecting the account value net of them double-counts.

Annual equivalence. Because the monthly decrement rates compound back to their annual values over a contract year, the fixed accrual compounds back to i_F and the nonforfeiture roll to i_nf, and every contractual step still happens once at the anniversary, the recursions collapse over any twelve months of one contract year to the annual-step recursions, term for term. Every anniversary value is therefore identical on the two grids, to floating point — AV, F, A, BB, RB, LW, MGV, phase, and l at each t = 12k. Nothing else agrees, and nothing else should: the claims, the expenses and the weight on the anniversary’s own cash are where the finer grid does its work.

Policyholder behavior modeling#

All dynamic formulas are std reference constructions; the qualitative and order-of-magnitude evidence is cited, and the tables that would calibrate them are behind paid subscriptions R9 REG-R62.

Base surrender table std — shape from R1: low early, rising through the surrender charge period, spiking at expiry, then falling back but staying above pre-shock levels.

Contract year (dur(t) + 1)

1–3

4–6

7–9

10

11 (shock)

12+

w_base

2%

3%

4%

5%

see below

6%

Shock lapse with rider suppression std — the single most important behavioral fact in the product. In the year the surrender charge expires the surrender rate was 10% with a GLWB rider versus 33% without R8:

w_shock = 0.33   no GLWB rider
w_shock = 0.10   GLWB in force but not activated
w_shock = 0.05   GLWB activated (phase = INCOME)

The third row extrapolates std from the qualitative finding that “contracts with GLWBs lapse less than those without” and “activated GLWBs lapse least,” with the lowest rates where the withdrawal is 95%–105% of the maximum R1. Applying a plain fixed-deferred shock lapse — reported at roughly 52%–56% for fixed-rate deferred annuities REG-R63 unverified — to an FIA with an in-force rider will materially understate the tail this product is sold for.

Rider moneyness multiplier std. Surrender is further suppressed when the guarantee is in the money:

M_money(t) = clamp( 1 − 0.6 × max(0, BB(t)/AV(t) − 1) , 0.2 , 1.0 )
w(t) = min( 0.35 , w_base(t) × M_shock(t) × M_money(t) ),   w(t) = 0 in DEPLETED

Rational surrender destroys a guarantee worth BB − AV in benefit-base terms; the observed direction is documented R1 R8, the functional form is not.

GLWB activation (utilization timing) std. Activation clusters at the required-minimum-distribution age R1 REG-R64 unverified, which makes the RMD regulations a behavioral input, not merely a tax one REG-R57 REG-R58:

h(a) = 0.00  for a < 60      h(a) = 0.05  for 60 ≤ a < rmd_age
h(a) = 0.40  at a = rmd_age  h(a) = 0.15  for a > rmd_age

with rmd_age = 73 std as a configurable model parameter — the statutory age is set by IRC §401(a)(9) as amended by SECURE 2.0 and finalized in T.D. 10001 REG-R57 REG-R58, is not printed in the retrieved research material, and must not be hard-coded. The deterministic base run activates at the model point’s income_start_age instead.

Withdrawal intensity given activation std. The majority of users withdraw 95%–105% of the maximum R1, and 37% of GLWB contracts took withdrawals in 2019–2020 versus fewer than 30% without a rider R8. Base assumption: withdraw exactly LW, with sensitivities at 0.95 and 1.05. The 1.05 case is an excess withdrawal and triggers the pro-rata reduction in step 5 — a 5% overdraw permanently reduces the guarantee, which is why efficiency and excess-withdrawal assumptions cannot be set independently.

Excess withdrawal incidence std: zero in the base run; any non-zero assumption must route through step 5 and the INCOME → TERMINATED attribution test [S1] [S5] [S9]. Additional premium std: none — deposits occur on 2.5% of contracts in years 2–10 and only 1.9% with a GLWB R8. Annuitization std: not modeled; where offered, payments are based on the greater of account value and cash surrender value — not the benefit base [S3] [S10], so annuitization is generally dominated by the GLWB [S3].

Worked example#

Anchor cell: Male 62 ANB, single life, P = $100,000, b = 7%, GLWB elected at issue, first lifetime withdrawal at anniversary 8 (attained age 70) — the anniversary that closes contract year 8, which on this grid is month t = 12 × 8 − 1 = 95, and that is the month the table below walks. Parameters as specified: c = 5.25% [S2], f = 0% [S1], φ = 0.95% [S9], g = 5.00% for years 1–10 [S2], m = 1.50 [S8] [S9], π(70, single) = 5.20% [S3], sc = 3% and v = 70% in contract year 8 [S5], i_nf = 1.00% std. The state opening contract year 8, at anniversary 7 — month t = 84, the model point’s first projected month (illustrative balances, broadly consistent with a seven-year deferral at these parameters) std: AV⁽⁰⁾ = 128,000.00 (100% indexed), BB⁽⁰⁾ = 180,000.00, RB⁽⁰⁾ = 100,000.00, MGV⁽⁰⁾ = 93,811.84 (= 87,500 × 1.01⁷), Wcum⁽⁰⁾ = 0. With no fixed allocation nothing accrues in months 84–94, so the eleven months before the anniversary carry only the decrements.

#

Item

Formula

Value

1

Index return over the contract year, R(95)

5,450 / 5,000 − 1

9.0000%

2

Credit rate cr(95)

max(0, min(5.25%, 9.00%))

5.2500%

3

Index credit IC(95)

128,000.00 × 0.0525

6,720.00

4

Account value after credit AV⁽¹⁾(95)

128,000.00 + 6,720.00

134,720.00

5

Rider charge Φ(95)

0.0095 × 180,000.00

1,710.00

6

Account value after charge AV⁽²⁾(95)

134,720.00 − 1,710.00

133,010.00

7

Guaranteed rollup rollup(95)

0.0500 × 100,000.00

5,000.00

8

Stacking credit stack(95)

1.50 × 6,720.00

10,080.00

9

Benefit base before step-up BB⁽³⁾(95)

180,000.00 + 5,000.00 + 10,080.00

195,080.00

10

Step-up test BB⁽⁴⁾(95)

max(195,080.00, 133,010.00)

195,080.00 (does not bind)

11

Lifetime withdrawal LW(95)

0.0520 × 195,080.00

10,144.16

12

Free withdrawal amount FW(95)

0.10 × 128,000.00

12,800.00

13

Excess E(95)

max(0, 10,144.16 − 10,144.16)

0.00 → no SC, MVA or clawback [S9]

14

Account value AV(95)

133,010.00 − 10,144.16

122,865.84

15

Guaranteed minimum value MGV(95)

93,811.84 × 1.01 − 10,144.16

84,605.80

16

Closing benefit base BB(95)

unchanged by a guaranteed withdrawal [S9]

195,080.00

Row 15 is worth reading twice on the finer grid. MGV accretes at (1 + i_nf)^(1/12) in each of months 84–95 and the withdrawal is deducted in month 95, so the twelve accruals multiply to exactly × 1.01 and the row is the annual arithmetic unchanged — while MGV(89), halfway through the year, is now a real number a mid-year surrender can be floored at rather than a value the annual grid never had.

Surrender test at the same anniversary. A full surrender of G = AV(95) = 122,865.84 with 12,800.00 − 10,144.16 = 2,655.84 of free amount remaining gives X = 120,210.00; SC = 3% × 120,210.00 = 3,606.30 [S5] [S10]; clawback = 0.30 × (0.07/1.07) × 120,210.00 = 2,359.26 [S10]; with i₀ = 3.00%, iₜ = 3.50% and n = 24 months remaining, MVA = 120,210.00 × [(1.03/1.035)² − 1] = 120,210.00 × (−0.00963850) = −1,158.64 [S10], inside the limit max(0, 122,865.84 − 5,965.56 − 84,605.80) = 32,294.48 [S10]. Net proceeds = 122,865.84 − 3,606.30 − 2,359.26 − 1,158.64 = 115,741.64, and CSV = max(115,741.64, 84,605.80) = 115,741.64.

Where the step-up binds. Under variant (a) — 3% simple rollup on RB, no stacking [S9] — the same cell opens contract year 8 with BB⁽⁰⁾ = 121,000.00, so Φ(95) = 1,149.50, AV⁽²⁾(95) = 133,570.50 and BB⁽³⁾(95) = 124,000.00. The step-up then binds: BB(95) = 133,570.50 and LW(95) = 0.0520 × 133,570.50 = 6,945.67. General result: the step-up matters when realised index credits outrun the guaranteed rollup, and is dominated whenever a stacking factor above 1.0 is present.

Where the liability lands. Holding index credits at zero from anniversary 8, the account value drains by LW + Φ = 10,144.16 + 0.0095 × 195,080.00 = 11,997.42 a year — one step a year, at the anniversary, not twelve — and is exhausted at the anniversary closing contract year 19, month t = 227, at attained age about 81. From that point the insurer pays $10,144.16 a year for the rest of the contract holder’s life, with no account value, no surrender value, no death benefit and no possibility of lapse [S1] [S3] [S9] R1. That stream is the guarantee.

Valuation and reserve pointers#

This library projects gross liability cash flows; reserve layers consume them and are cited, not reproduced.

  • Formulaic statutory (CARVM). AG 33 — printed title “Determining CARVM Reserves for Annuity Contracts With Elective Benefits” — constructs and values the integrated benefit streams for annuity contracts with elective benefits; AG 35 specifies how the index feature enters that greatest-present-value calculation, through four computational methods with quarterly certification and change-notification requirements, “Type 1” and “Type 2” being the guideline’s own printed section headings, not industry shorthand REG-R151 REG-R152. Both texts have now been read in full from the AP&P Manual Appendix C print — a free download, not the paid publication recorded earlier REG-R33 — so their mechanics are no longer unverified; titles and continued incorporation remain independently confirmed by the VM-C index REG-R41. AG 33’s effective date, recorded on both sides because the two do not reconcile: its own Effective Date block reads “This guideline shall be effective on December 31, 1998, affecting all contracts issued on or after January 1, 1981”, with a grade-in of 33⅓ / 66⅔ / 100% that completed on December 31, 2000 and therefore has no live effect on any current valuation REG-R151; the library elsewhere carries December 31, 1995 for a differently-titled instrument from IRS Rev. Rul. 2002-6. The 1981 issue-date reach is common to both, the extracted pages carry no amendment history, and the reconciliation is unresolved — that the guideline was later revised is an inference, not something either source states. AG 35 prints no date at all; its only temporal language is “regardless of the date of issue” REG-R152. Two documents in this chain remain unavailable and are named rather than glossed: AG IX-B, which AG 35 points at three times as an alternative source of the valuation interest rate for an indexed contract and which this library holds only as a VM-C index entry REG-R41 REG-R152, and the NAIC Interest-Indexed Annuity Contracts Model Regulation, Sections 5 and 6 of which AG 35 supersedes and which is not in this library at all REG-R152.

  • Principle-based statutory. VM-22, effective for valuation dates on or after January 1, 2026, with a three-year elective transition and mandatory prospective application three years after the effective date REG-R36; the Academy paper states elective 1/1/2026 and required 1/1/2029 R1; the VM-22 (A) Subgroup handles post-launch monitoring R7. An FIA sits in the Accumulation reserving category, which expressly includes fixed income streams from guaranteed living benefits after account exhaustion — the DEPLETED phase of this model — and GLB utilization risk is named among the risks to be reflected; the stochastic reserve is CTE70 REG-R36. Maximum valuation interest rates for formulaic income-annuity reserves are in VM-V Section 1, not VM-22 REG-R36 REG-R37. Enabling statute: Model #820 REG-R1; parent document REG-R3.

  • Asset adequacy. ASOP No. 22, meaning the same projection must serve CARVM and cash flow testing REG-R29 REG-R27. AG 35 does not itself impose the requirement — it directs that reserves be tested “to the extent required by law, regulation, or regulatory requirements” REG-R152. The operative NAIC requirement is VM-30, with SVL §6.B, codified as A-822 ¶3, behind it, and any shortfall becomes an additional reserve REG-R100 REG-R1 REG-R153.

  • Nonforfeiture floor. Model #805 §4 and Model #806 §7 as implemented in step 6 R2 R3 REG-R42.

  • Tax reserve. IRC §807: the greater of net surrender value and 92.81% of the NAIC-prescribed method — CARVM for annuities — capped at the statutory reserve REG-R16.

  • GAAP (LDTI). The index feature is an embedded derivative, fair-valued on expected current and future index credits (current index period closed-form Black-Scholes); the GLWB is a market risk benefit at fair value with an adjustment for explicit fees; remaining cash flows form the host contract discounted at a host accrual rate set so the total liability at issue equals the premium; DAC, DSI and URL are the intangibles R1 REG-R34 REG-R71.

  • Standards for the modeling work. ASOP No. 56 (modeling) REG-R32; ASOP No. 54 (pricing, if a profit-metric mode is added) REG-R70; ASOP No. 2 for any NGE re-declaration logic R6 REG-R26.

Key sensitivities and model risks#

Dominant assumptions, in rough order of impact on the value of the guarantee:

  1. GLWB activation timing and intensity. The liability is a function of when the holder starts and whether they take 95%, 100% or 105% of the maximum R1 R8 REG-R64 REG-R67; activation five years earlier compounds directly into the depletion date.

  2. Surrender, specifically the rider-suppressed shock lapse. 10% versus 33% in the shock year R8 governs how much of the block survives to reach DEPLETED at all. Applying a fixed-deferred shock lapse to a rider-in-force FIA is the most consequential error available here.

  3. Longevity in the DEPLETED phase. The payment is a life annuity written at a payout percentage set decades earlier: use the 2012 IAM/IAR family with Scale G2 REG-R59 REG-R60 and test against the 2020–2024 payout experience REG-R61; deferred-period annuitant mortality, which governs who reaches the income phase, is served publicly by only two dated studies REG-R65.

  4. Cap re-declaration and the option budget. The declared cap drives the account value, the stacking credit and hence the benefit base; it is an NGE reset against the option budget R1 R6 REG-R26 REG-R68. Holding the snapshot cap constant for 40 years is a strong implicit assumption.

  5. Benefit base growth form. Blended versus pure rollup versus pure stacking changes both the level of the guarantee and its correlation with index performance; pure stacking shifts the deferral guarantee from insurer to market and is materially cheaper to hedge [S3] [S4].

Known pitfalls:

  • The behavioral assumptions above must not be reused in a CARVM valuation. Every dynamic lapse, activation, utilization and excess-withdrawal formula in “Policyholder behavior modeling” is an experience assumption. AG 33 states that for elective benefits “incidence rates should not be based on tables reflecting past company experience, industry experience or other expectations” — the elective assumption is not an assumption at all but a decision variable maximised over, with all rates between 0% and 100% theoretically in scope and the greatest present value typically occurring at 0% or 100% REG-R151. Wiring the projection’s behavior module into the reserve run is a silent compliance error. The non-elective side is the opposite case: incidence comes from the SVL-prescribed tables where one exists, otherwise from company or industry experience with margins for conservatism (unquantified), and the SVL-prescribed annuity mortality table discounts every payment in every integrated benefit stream for survivorship — the elective surrender and withdrawal streams included, so a cash-value stream is not valued on a mortality-free basis REG-R151.

  • “Efficient policyholder selection” is not AG 33’s language and should not be attributed to it. The phrase appears nowhere in the guideline; the actual construction is the prohibition, the trial sets, and the direction to “consider, not necessarily test” all potential integrated benefit streams REG-R151.

  • The 0% floor is on the index credit, not the account value. Rider charges and strategy fees can exceed interest credited, “which would result in loss of premium” [S7]. Flooring the account value silently removes the charge drag that produces depletion.

  • The clawback factor is b/(1+b), not b [S10] — the account value already contains the bonus; using b over-recovers by (1+b).

  • The “simple rollup” is a flat dollar increment, on premium less withdrawals [S2] or on the adjusted initial base [S9] — never simple interest on the current grown base. Compounding it inflates the base and every downstream charge and payment.

  • Attribution at depletion. Survival of the income stream depends on the cause [S1] [S5] [S9]; a model testing only AV ≤ 0 will either give the guarantee away after an excess withdrawal or destroy it after a legitimate one.

  • No lapse in DEPLETED. Leaving the surrender decrement on silently truncates the most expensive part of the liability.

  • Rider charge base and ordering. The charge is on the benefit base, not the account value [S1] [S2] [S9], and is taken after index credits [S9]. In the worked example the benefit base closes at 1.59× the account value at anniversary 8 (195,080.00 against 122,865.84), so charging on the account value understates the deduction by a growing margin.

  • Excess-withdrawal denominator. Post-exercise it is the account value net of the guaranteed amount [S9]; pre-exercise it is the gross account value [S1] [S3] [S5] [S9] — the two differ by exactly LW.

  • MVA sign and collar. Negative when yields rise [S10]; applies only above the free amount, only inside the MVA period, never to the death benefit, never below the nonforfeiture minimum [S1] [S5] [S6] [S7] [S10]. The linear form (i₀ − iₜ) × T [S6] [S7] is unbounded and must be collared separately; the ratio form used here is not.

  • Monthly-sum floor convention is ambiguous. The Academy’s worked example applies a 0% monthly floor as well as a 1% monthly cap R1, which is unusual — most monthly-sum designs cap the upside monthly but let negative months subtract in full, and one rate sheet declares a 1.70% monthly cap with a 0.50% guaranteed minimum without stating the floor [S4]. Verify against a contract before implementing that variant.

  • Interim values and index costs. The baseline has none; adding one requires a different structure — a Daily Account Value / Protected Account Value with a 90% protection level [S10] or a daily-tracked strategy value [S11], both daily marks of the embedded option rather than interpolations. Proprietary volatility-controlled indices separately deduct embedded servicing, transaction and financing costs (0.50% p.a. at BNPP MAD 5 and AiPEX [S2]; 2 bp change-in-notional plus 12 bp annualized replication at S&P 500 Dynamic Intraday TCA [S10]), which reduce R(t) before the cap or participation rate.

  • Stale and state-varying parameters. Declared rates are dated 07/01/2022 [S2] and the access date [S4]; one carrier’s rate sheets [S-f1], another’s official host [S-f3] and a third’s current brochure [S-f4] could not be fetched. State variation in surrender charges, vesting, MVA availability and waiver terms is extensive and deliberately not modeled [S2] [S3] [S6] [S7].