Technical Notes#

Status: Draft, 2026-08-04; AP&P Manual appendix material added 2026-08-06. All cited sources accessed 2026-08-04 except REG-R151 (AG 33), REG-R153 (A-820), REG-R156 (A-250) and REG-R157 (A-255), accessed 2026-08-06.

Scope note. These notes specify a reference liability cash-flow projection model for the standardized composite product defined in product-spec.md (same directory). It is not any single insurer’s product. [S#]/[R#] tags resolve against _research/variable-annuity.md; [REG-R#] tags resolve against the single shared cross-product numbering space R1–R157 curated at references/regulatory-and-actuarial-references.md (R1–R34 from _research/regulatory-actuarial.md, R35–R72 from _research/regulatory-actuarial-annuities.md, and R151–R157 the AP&P Manual appendix items read at first hand on 2026-08-06 — of which four are cited here, AG 33 REG-R151, A-820 REG-R153, A-250 REG-R156 and A-255 REG-R157 — with most of the R73–R149 block unused). std marks a standardization introduced for the reference implementation; unverified marks a claim the research file could not confirm against a retrieved document. Every parameter value below is identical to the value in product-spec.md. The mechanics anchor is the Jackson Perspective II chassis S1 S2 S3.

Relationship to sibling documents. The separate-account charge-accrual convention — a monthly discretization of daily fund-expense and asset-charge accrual, (1 + r)(1 − e/12)(1 − m/12) — is specified once in products/variable_ul/technical-notes.md and reused here. Two qualifications, because that file is a life file: it applies the convention to subaccount values directly and never carries a unit count, whereas the unit ledger AV = Σ U_i V_i used below is written out here in full; and its charge stack includes a cost of insurance on a net amount at risk and an IRC §7702 corridor, neither of which exists in a VA — a VA’s guarantees are instead a GMDB benefit base and a GLWB benefit base, shadow accounts that never fall with the market. Nothing on the life side’s NAAR/corridor path may be carried across. Generic GLWB machinery is shared with products/fixed_indexed_annuity/technical-notes.md (sibling deliverable in this library) and referenced rather than restated where the two products agree — namely activation timing (that file’s RMD-clustered activation hazard), RMD relief, and the post-depletion phase. Two items on that list are not shared and are written out below: that file carries no cohort construction (the cohort method used here is VM-21’s R1), and its excess-withdrawal rule reduces the benefit base pro rata on the excess only, with no dollar-for-dollar reduction for the guaranteed portion — whereas the Jackson GWB is reduced dollar-for-dollar by the non-excess portion first. The one structural difference is decisive: in an FIA the account value is driven by a floored index-credit formula, whereas here separate-account performance drives the account value directly and can fall without limit, so the guarantee is far more path-dependent and its cost cannot be obtained from a deterministic run.

Model scope and conventions#

  • Purpose. Project gross liability cash flows — premium, withdrawals, surrender proceeds, death benefits, insurer-funded post-depletion GLWB payments, charge income and expenses — for a single-contract model point, per scenario. Reserves are not computed (see Valuation and reserve pointers).

  • Projection frequency: monthly std. The base contract charge is contractually assessed daily as a percentage of the average daily account value of the Investment Divisions S2; the model applies one-twelfth of the annual rate at each month end std. Do not also compound daily — pick one discretization and document it, because reconciling to an admin system requires knowing which was used.

  • Event calendar. Contract Quarterly Anniversaries fall at the end of months t ≡ 0 (mod 3); Contract Anniversaries at the end of months t ≡ 0 (mod 12) std. Rider charges are assessed at the end of a contract quarter, following the disclosed rule that the first deduction occurs at the end of the first quarter following election S4 / on the three-month anniversary of the rider effective date S8.

  • Timing convention. Within month t: policyholder transactions at the beginning of the month (BOM); unit value growth over the month; charges, guarantee-base events and decrements at the end of the month (EOM) std.

  • Age basis: age nearest birthday (ANB) std. Rationale: VM-21 prescribes the 2012 IAM Basic Table (improved to Dec. 31, 2017 on Scale G2) for standard-projection mortality R1, and the 2012 IAM Period Table it underlies is printed age nearest birthday REG-R59; and the GAWA%, GMDB roll-up and step-up eligibility bands are all attained-age lookups S1 S3.

  • Model points. Single-contract model points projected on an expected (probability-weighted) basis; survivorship factors multiply per-contract cash flows. No aggregation, no cohort splitting except the utilization cohorts described below.

  • Scenarios. Subaccount gross returns are exogenous per-scenario inputs; see Stochastic requirement.

  • Rounding. Full precision carried internally; reported cash flows to cents std.

Model point attributes#

Attribute

Type

Example (anchor cell)

issue_age

int (ANB)

60 std

sex

enum {M, F}

M std

designated_lives

enum {single, joint}

single std

tax_status

enum {NQ, Q}

NQ std

premium_single

currency

100,000 std

premium_tax_rate

rate

0.000 std, within 0.0%–3.5% S2

alloc[i]

vector, sums to 1

(0.60, 0.40) std

fund_expense[i]

annual rate

(0.0095, 0.0065) std, within 0.52%–2.28% S2

glwb_option

enum {Value, Core, Plus}

Core S3

glwb_stepup_basis

enum {annual_CV, highest_quarterly_CV}

annual_CV S3

gmdb_option

enum {basic, rollup, HQAV, combination}

rollup S3

cdsc_schedule

vector by completed years since premium receipt

8.5/7.5/6.5/5.5/5.0/4.0/2.0/0.0 % S2

rate_sheet_date

date (first-class assumption)

2026-04-27 S3

issue_date

date

—

av_initial, gwb_initial, bb_initial, rb_initial

currency (in-force cells)

0 / 0 / 0 / 0 at issue

State variables#

Variable

Description

Updated

U_i(t)

units held in subaccount i

on every unit purchase/cancellation

V_i(t)

unit value of subaccount i

monthly growth

AV(t)

contract value = Σ_i U_i(t)·V_i(t)

derived

GWB(t)

Guaranteed Withdrawal Balance (GLWB benefit base) S1

premium, withdrawal, bonus, step-up, adjustment

GAWA(t)

Guaranteed Annual Withdrawal Amount S1

fixed at first withdrawal; excess withdrawals, step-ups, bonus, premium

BB(t)

Bonus Base S1

premium, excess withdrawal, step-up

bonus_end(t)

Contract Anniversary on which the Bonus Period ends S1

restarts on a Bonus-Base-increasing step-up

ADJ(t)

GWB Adjustment amount S1

premium; consumed or voided on the GWB Adjustment Date

RB(t)

GMDB roll-up Benefit Base S1

annual roll-up; year-end withdrawal adjustment; premium

NP(t)

cumulative Net Premiums (a GMDB floor) S1

premium

RP(t)

Remaining Premium (the CDSC basis) S2

premium; withdrawal of premium incl. charges

SumW_y

cumulative withdrawals in the current Contract Year S1

withdrawal; reset each anniversary

gawa_pct_fixed

GAWA% locked at the first withdrawal by attained age S1

once

forlife_flag

For Life Guarantee in effect (true from issue at age 59½+) S1

once

depleted_flag

AV has reached zero with the GLWB in force S1

once

phi_G(t), phi_D(t)

current GLWB / GMDB charge rates

fifth-anniversary reset S1

l(t)

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

monthly decrements

Assumption inputs#

Three classes are distinguished explicitly, because they behave differently under governance: (a) cannot be changed by the insurer; (b) can, subject to ASOP No. 2 discipline for non-guaranteed elements, which expressly covers variable deferred annuities REG-R26; (c) is the modeler’s view and must be justified under ASOP No. 56 REG-R32.

(a) Contractual / guaranteed elements#

Input

Value

Basis

Maximum base contract asset charge

1.30% p.a. of average daily separate-account value

S2

Maximum annual contract maintenance charge

$35, waived at contract value ≥ $50,000

S2

CDSC schedule (by completed years since premium receipt)

8.5 / 7.5 / 6.5 / 5.5 / 5.0 / 4.0 / 2.0 / 0.0 %

S2

Free withdrawal

10% of Remaining Premium per Contract Year, minus earnings; earnings out first

S1

No CDSC on withdrawals within the GLWB annual limit

—

S1

Excess-withdrawal algebra (GWB, GAWA)

dollar-for-dollar then pro rata

S1

GMDB withdrawal adjustment

d-f-d up to ρ × RB(prior anniversary), pro rata above, applied at Contract Year end

S1

Benefit base caps

GWB and Bonus Base capped at $10,000,000

S1

GMDB growth cutoff

Contract Anniversary preceding the oldest Covered Life’s 81st birthday

S1

For Life Guarantee trigger

Designated Life 59½ or older

S1

Guaranteed maximum GMDB charge

1.80% p.a. of the GMDB Benefit Base

S2

Guaranteed maximum GLWB charge

3.00% p.a. of the GWB

std, observed 1.20%–3.00% by option/vintage S1

Maximum single GLWB charge increase

+0.25% (Core tier)

S1

Charge-increase frequency

each fifth Contract Anniversary, with irrevocable opt-out

S1

Latest Income Date

Contract Anniversary at owner age 95

S2

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

Snapshot dated 2026-04-27, the Jackson rate sheet date S3. Rate sheets carry an explicit “can be superseded at any time” clause with a 10-day advance-filing commitment S3 S5 S8, so the rate-sheet date is a first-class model input, not metadata.

Input

Value

Basis

Current base contract asset charge

1.30% p.a. (= the contractual maximum)

S2

— M&E component m

1.00% p.a.

std decomposition (see spec footnote 6)

— administrative component α

0.30% p.a.

S7 component; split std

Current GLWB charge phi_G

1.25% p.a. of GWB

S3

Current GMDB charge phi_D

0.90% p.a. of RB

S2 S3

Bonus percentage b

6.00% of Bonus Base

S3

GMDB roll-up percentage ρ

6.00% (age ≤ 69 at election); 5.00% (age ≥ 70)

S3

GWB Adjustment percentage s

105%

S3

GAWA% grid g(a) (Single, Core)

35–59: 4.00%; 60–64: 4.00%; 65–69: 5.55%; 70–74: 5.75%; 75–80: 5.95%; 81+: 6.20%

S3

Fund expenses e_i

0.95% equity / 0.65% fixed income

std within 0.52%–2.28% S2

Optional variant modules, each fully parameterized by cited values. (i) VIX-linked fee reset: phi(k) = phi_0 + 0.05% × [avg(VIX²)/33 − 10], clipped to ±0.40% p.a. per quarter and to [0.60%, 2.50%], quarterly deduction = annual ÷ 4 S4 S6. (ii) Treasury-linked roll-up rate: 20-day average 10-year CMT ending the 15th of the last month of the prior quarter, +1.00% (or +1.50% before the first withdrawal), rounded to 0.10%, floored 4%, capped 8% S7. (iii) Two-table post-depletion payout, Table A while AV > 0 and a lower Table B once AV = 0 S8.

Cash flow components and recursions#

Notation (defined once, used throughout and consistent with product-spec.md)#

Symbol

Meaning

t

policy month index, t = 1, 2, …; y = ceil(t/12) contract year; k = ceil(t/3) contract quarter

x

issue age (ANB) = 60 std; attained age a(t) = x + y − 1

i

subaccount index, i ∈ {1, 2} (1 = equity, 2 = fixed income)

U_i(t), V_i(t)

units and unit value; SA_i(t) = U_i(t)·V_i(t); AV(t) = Σ_i SA_i(t)

w_i(t)

value weight SA_i(t) / AV(t) (the pro-rata deduction key)

r_i(t)

gross fund return of subaccount i over month t (scenario input)

e_i

annual fund expense ratio (0.0095, 0.0065) std

m, α

annual M&E 0.0100 std and administrative asset charge 0.0030 S7; m + α = 0.0130 S2

P(t), τ

gross premium at BOM t; premium tax rate 0.000 std (range 0–3.5% S2)

W(t)

gross withdrawal, measured inclusive of withdrawal charges, MVAs, advisory fees and other charges for all guarantee calculations S1

E(t), N(t)

excess and non-excess portions of W(t) S1

L(t)

annual withdrawal limit = max(GAWA(t), RMD(t)) (RMD term active only for qualified contracts) S1

c(t)

contingent deferred sales charge on W(t) S2

f_c

annual contract fee $35, waived at AV ≥ 50,000 S2

phi_G, phi_D

annual GLWB (0.0125) and GMDB (0.0090) charge rates S3

b, ρ, s

bonus 0.0600, GMDB roll-up 0.0600, GWB Adjustment 1.05 S3

g(a)

GAWA% at attained age a S3

M(t)

in-the-moneyness ratio (benefit base ÷ account value)

λ(t)

dynamic lapse multiplier

q^d(t), q^w(t)

monthly mortality and surrender rates; l(t) in-force probability

Monthly conversions std: asset charges use simple annual/12 (matching the average-daily-value accrual S2); decrements use 1 − (1 − q_annual)^(1/12); the GMDB roll-up and GLWB bonus are credited annually at the Contract Anniversary, matching the contract S1.

Dimensional check: phi_G/4 × GWB is currency per quarter; m/12 × SA_i is currency per month; g(a) × GWB is currency per year; E(t)/CV is dimensionless.

Account value and unit mechanics#

AV(t) = Σ_i U_i(t) · V_i(t)

Unit value (monthly discretization of a daily accrual [S2]) [std]:
V_i(t) = V_i(t−1) · (1 + r_i(t)) · (1 − e_i/12) · (1 − (m + α)/12)

Charges assessed per unit of value (fund expenses, M&E, administrative asset charge) live inside V_i; charges assessed per contract or on a benefit base are collected by cancelling units, leaving V_i untouched — ΔU_i = C · w_i(t) / V_i(t), so ΔAV = C std. The pro-rata key is cited for the annual contract maintenance charge, “deducted proportionally” S2; extending it to the rider charges is std (spec footnote 8).

Charge stack with exact assessment bases#

Charge

Rate

Assessment base

Frequency

Mechanism

Fund expense

0.95% / 0.65% p.a. std

fund net assets

daily → monthly std

inside unit value (paid to the fund, not the insurer)

M&E risk charge

1.00% p.a. std

average daily separate-account value

daily → monthly std

inside unit value

Administrative asset charge

0.30% p.a. S7

average daily separate-account value

daily → monthly std

inside unit value

Annual contract fee

$35, waived at AV ≥ $50,000 S2

per contract

Contract Anniversary S2

unit cancellation, pro rata S2

GLWB rider charge

1.25% p.a. S3

GWB (benefit base), not account value S1 S3

quarterly at rate/4 S1

unit cancellation, pro rata std

GMDB rider charge

0.90% p.a. S2 S3

GMDB Benefit Base S3

quarterly at rate/4 std

unit cancellation, pro rata std

CDSC

8.5%→0.0% by completed years since premium receipt S2

Remaining Premium withdrawn S2

on withdrawal

netted from withdrawal proceeds

Premium tax

0.0% base std, 0.0–3.5% range S2

premium

at premium / annuitization S2

deducted from premium

The single most important structural point about this stack: the two rider charges are levied on benefit bases that rise when markets fall, so rider income is naturally counter-cyclical — until account value reaches zero, at which point the fee stops S4 precisely when the guarantee is paying. A model that keeps charging after depletion overstates revenue in exactly the scenarios that drive the CTE70 tail.

Monthly processing order#

At BOM of month t:

  1. Advance y, k, a(t); reset SumW_y if a new contract year began. If depleted_flag is set, run the post-depletion routine (step 9) and skip steps 2–7.

  2. Premium. Net premium P(t)·(1 − τ) buys units at V_i(t−1) per alloc[i]. Then S1: GWB += P(1−τ); BB += P(1−τ); NP += P(1−τ); RP += P(t); RB += P(1−τ) (premiums received in the first Contract Quarter are treated as of the Issue Date S1); if a first withdrawal has already occurred, GAWA += g(a_first) · P(1−τ), or g × ΔGWB if the $10m cap binds S1. ADJ increases by s · P(1−τ) for premiums before the first anniversary after endorsement and by P(1−τ) for later premiums S1.

  3. Withdrawal. Given W(t), in this order — the first bullet must run before L is formed, or a first withdrawal would be tested against GAWA = 0 and score entirely as excess:

    • If this is the first withdrawal, fix gawa_pct_fixed = g(a(t)) and set GAWA = g(a(t)) · GWB on the pre-withdrawal GWB S1; mark the year as bonus-ineligible S1; void ADJ S1.

    • SumW_y += W(t); L = max(GAWA, RMD); E = min(W, SumW_y − L) if SumW_y > L else 0; N = W − E S1.

    • CDSC. Charge-free amount = earnings max(0, AV − RP) plus max(0, 0.10·RP − earnings), i.e. 10% of Remaining Premium with earnings coming out first S1; aged-out premium is free S1; no CDSC applies to cumulative withdrawals within L S1. On the chargeable portion apply the schedule by completed years since receipt of the premium being withdrawn S2.

    • Cancel units pro rata for W(t) (which is gross of all charges S1); reduce RP by the premium portion withdrawn including withdrawal charges S2.

    • GLWB base update (CV_pre = AV after N has been deducted):

      If SumW_y ≤ L:  GWB ← max(GWB − W, 0);  GAWA unchanged
If SumW_y > L:  GWB ← max( (GWB − N) · (1 − E / CV_pre) , 0 )
                GAWA ← min( GAWA · (1 − E / CV_pre) , GWB )
                BB   ← min( GWB , BB )                        [S1]

    • GMDB adjustment is accrued, not applied: record the withdrawal against the year-to-date allowance ρ · RB(prior anniversary); the adjustment is applied at the end of the Contract Year S1.

  4. Unit value growth over month t per the formula above.

  5. EOM quarterly charges (t ≡ 0 mod 3): Fee_G = (phi_G/4)·GWB, Fee_D = (phi_D/4)·RB; cancel units pro rata S1 S3.

  6. EOM annual contract fee (t ≡ 0 mod 12): f_c if AV < 50,000, cancelled pro rata S2.

  7. EOM anniversary guarantee events (t ≡ 0 mod 12), in this order std:

    1. Apply the accrued GMDB withdrawal adjustment: dollar-for-dollar up to ρ · RB(prior anniversary), then RB × (proportional CV reduction from the excess) S1.

    2. GMDB roll-up: if a(t) is at or before the anniversary preceding the oldest Covered Life’s 81st birthday, RB ← RB · (1 + ρ) S1.

    3. GLWB bonus: if no withdrawal occurred in contract year y and y ≤ bonus_end, GWB ← GWB + b · BB; if after the first withdrawal, GAWA ← max(g · GWB, GAWA_before_bonus) S1. The bonus does not change BB or ADJ S1.

    4. Step-up: if AV > GWB, then GWB ← AV; BB ← max(GWB, BB); restart the Bonus Period (bonus_end ← y + 10) if the step-up occurs on or before the anniversary following the Designated Life’s 80th birthday S1; if after the first withdrawal, GAWA ← max(g · GWB, GAWA) S1.

    5. GWB Adjustment Date test — at the later of the anniversary on/after age 70 and the 12th Contract Anniversary, if no withdrawal has ever been taken then GWB ← max(GWB, ADJ) and the provision terminates S1.

    6. If forlife_flag is false and GWB < GAWA, set GAWA = GWB S1.

    7. Cap GWB and BB at $10,000,000 S1.

  8. Depletion test. If AV ≤ 0 and the GLWB is in force, set depleted_flag. If the GAWA% has not yet been fixed, fix it at the percentage for the attained age when contract value hits zero S1. All other endorsements terminate without value and no death benefit is payable on subsequent death S1.

  9. Post-depletion routine. With forlife_flag true, pay GAWA at each Contract Anniversary for the life of the Designated Life S1. Without it, pay GAWA until the earlier of death and GWB depletion, truncating the final payment to the remaining GWB and decrementing GWB by each payment S1.

  10. EOM decrements — death first, then surrender std: l(t) = l(t−1) · (1 − q^d(t)) · (1 − q^w(t)).

Step-order caveat. The research file does not settle whether the year-end bonus is credited before or after the anniversary step-up test S1. The std order above (bonus, then step-up) yields GWB_new = max(GWB_old + bonus, AV); the reverse yields max(GWB_old, AV) + bonus, which is strictly more generous. The std choice follows the one design in the set that states the interaction explicitly — Lincoln’s, where “an Enhancement and an Account Value Step-up cannot both occur in the same year; if the step-up is ≥ the Enhancement, the Enhancement is not applied” S8. Treat the alternative as a first-order sensitivity, not a rounding issue.

Guaranteed minimum death benefit#

DB(t)          = max( AV(t) , NP(t) , RB(t) )                          [S1]
GuaranteeClaim = max( 0 , GMDB_guarantee(t) − AV(t) )
               = max( 0 , max(NP(t), RB(t)) − AV(t) )

DB(t) is the gross claim outflow; GuaranteeClaim is the net general-account strain. Both are needed and they are not interchangeable — projecting only the guarantee excess as the claim understates gross benefit outgo and breaks reconciliation with statutory exhibits, while projecting both double counts. The full argument is set out once in products/variable_ul/technical-notes.md; its logic carries over, but that file states it for a life contract, where the gross outflow is the death benefit less policy debt and the net strain is the net amount at risk. A VA has neither policy debt nor a NAAR: the gross outflow here is DB(t) and the net strain is max(0, guarantee − AV), as set out above.

The three GMDB guarantee forms and their recursions std naming; mechanics cited:

Form

Recursion

Withdrawal treatment

Source

Return of premium (proportional)

G(t) = G(t−1) + P(1−τ)

G ← G · (1 − W/AV_pre) — proportional, not dollar-for-dollar

S1 S2; same design at S4 S7

Annual ratchet / highest anniversary value

G(t) = max(G(t−1), AV(t)) at each anniversary (quarterly anniversaries in the HQAV variant), growth ceasing at the age cutoff

proportional

S1 (HQAV, quarterly, to age 81); S4 (Maximum Anniversary Value); S7 (to age 85)

Fixed roll-up (representative)

RB(t) = RB(t−1) · (1 + ρ) at each anniversary until the cutoff

d-f-d up to ρ · RB(prior anniv.), pro rata above, applied at year end

S1 S3

Combination

max(roll-up component, ratchet component), each as above

as above

S1

Cash flow outputs (per contract, month t, before survivorship weighting)#

Cash flow

Formula

Sign

Premium income

P(t)

+

Charge income — M&E and admin

Σ_i SA_i^{pre-charge}(t) · (m+α)/12

+

Charge income — rider fees

(phi_G/4)·GWB + (phi_D/4)·RB at quarter ends

+

Charge income — contract fee

f_c at anniversaries when AV < 50,000

+

Charge income — CDSC

c(t)

+

Death benefit (gross)

DB(t)

−

Death benefit (net GA strain, memo)

max(0, max(NP, RB) − AV)

memo

Surrender proceeds

AV(t) − CDSC on surrender

−

Withdrawal proceeds

W(t) − c(t)

−

Post-depletion GLWB payments

GAWA at each anniversary while in the depleted state

−

Maintenance expense

[100 · 1.025^(vy−2015)]/12 + (0.0007/12)·AV(t) R1

−

Aggregate expected flows weight by l(t−1) (charges, premiums, expenses), l(t−1)·q^d(t) (death) and l(t−1)·(1 − q^d(t))·q^w(t) (surrender) std.

Stochastic requirement — the scenario interface#

Guarantee cost cannot be valued deterministically. VM-21 makes this structural: the Alternative Methodology is available only for a group of variable deferred annuity contracts with either no guaranteed benefits or only GMDBs — never for a GLWB block R1. The base deterministic run specified in the worked example below is a mechanics demonstration only; it verifies the recursion, not the value of the guarantees.

Real-world scenarios — for liability cash flow projection. The interface is a set of per-scenario, per-subaccount, per-month gross returns r_i(t, ω). VM-21 requires each variable subaccount to be mapped to an appropriately crafted proxy fund, normally a linear combination of recognized market indices, sub-indices or funds reflecting efficient-frontier characteristics R1. Projections of accumulated deficiency ignore federal income tax in both cash flows and discount rates and must reflect company expenses including overhead and investment expense, fund expenses, contractual fees and charges, revenue-sharing income net of expenses, and reinsurance and hedging cash flows; cash flows from any fixed account options, and any market value adjustment on projected withdrawals or surrenders, must also be included R1.

Risk-neutral scenarios — for hedging and fair value. A separate, market-consistent set is required for hedge valuation under a Clearly Defined Hedging Strategy (VM-21 §9) REG-R35 and for the fair value of the GLWB/GMDB as market risk benefits under LDTI [REG-R34 — unverified, source not fetched (fasb.org 403); summary-based](#uslib-reg-r34) REG-R71. The two sets are not interchangeable; the model exposes the scenario basis as an input, never as a hard-coded assumption.

Reserve layer, cited not reproduced. CTE70 for the reserve, CTE(98) for capital, on the same projection R1 R3 REG-R35; see Valuation and reserve pointers.

Prescribed-assumption anchor. VM-21 §6.C’s Guarantee Actuarial Present Value is the regulator’s own moneyness construction and the most useful public calibration anchor available: assume immediate or continued exercise if the benefit is exercisable, otherwise exercise at the earliest possible time; once a GMWB is exercised, withdraw 100% of the guaranteed maximum annual amount each subsequent year; account value growth 0% net of all fees; any market index held constant; mortality on the 2012 IAM Basic Table improved to December 31, 2017 with Scale G2 and no further improvement; discounting at the 10-year Treasury bond rate on the valuation date R1.

Policyholder behavior modeling#

All dynamic forms below are std compositions of cited components.

Dynamic lapse on moneyness — the single most important behavioral assumption#

Define the in-the-moneyness ratio as benefit base ÷ account value:

M_G(t) = GWB(t) / AV(t)                    (living benefit)
M_D(t) = max(NP(t), RB(t)) / AV(t)         (death benefit — the guarantee actually
                                            floored under `DB`, not `RB` alone)

Apply the only closed-form dynamic lapse formula the Valuation Manual publishes for VAs — the VM-21 §7.B.1 Alternative Methodology multiplier, stated there with GV/AV where GV is the GMDB R1:

λ(M) = min[ U , max( L , 1 − Mult · (M − D) ) ],
       with U = 1.00, L = 0.50, Mult = 1.25, D = 1.10                  [R1]

q^w_annual(t) = min[ 1 , q^w_base(y) · λ*(t) · κ(t) ]                  [std composition]

where λ*(t) = min( λ(M_G(t)) , λ(M_D(t)) )   — the contract carries both a VAGLB and a
    GMDB, and VM-21 §6.C.6 directs that such contracts use the **lower** of the two
    ITM-based rates [R1];
and   κ(t) = 0.60 in any contract year with a projected withdrawal, else 1.00 [R1];
and   q^w_annual(t) = 0 whenever AV(t) = 0 [R1].

q^w_base(y) is the VM-21 Table 6.3 “under 50% ITM” column std: 4.0% p.a. during the surrender-charge period (contract years 1–7 here S2), 25.0% in the first year after it (year 8), 15.0% thereafter R1. Monthly conversion 1 − (1 − q^w_annual)^{1/12} std.

Caution: the multiplier and the table are two different cited constructions of the same effect. The multiplier floors suppression at 50%, whereas Table 6.3’s own ITM grading runs from 25.0% to 4.0% between the “<50%” and “>200%” rows in the first year after the surrender charge period — an 84% suppression R1. Compose them as here, or replace the multiplier with a direct table lookup; do not apply both gradings at once. The economic anchor for the size of the effect is the FIA experience split: in the year the surrender charge expires, surrender was roughly 10% with a GLWB rider versus 33% without [REG-R62 — unverified, from press coverage of the 2019–20 study](#uslib-reg-r62).

GLWB utilization#

The activation-timing machinery — an RMD-clustered activation hazard — is documented in products/fixed_indexed_annuity/technical-notes.md and reused here. The cohort construction below is VM-21’s R1, not that file’s: it carries no cohort machinery. Parameterized here by:

  • First-withdrawal age. Base run std: age 70, on the finding that activation clusters at the RMD age [REG-R64 — unverified](#uslib-reg-r64) REG-R57 REG-R58. The prescribed alternative is VM-21’s Withdrawal Delay Cohort Method, which splits the contract into cohorts weighted by differences in a revised GAPV across candidate initial withdrawal ages, discarding cohorts below the attained age and rescaling R1.

  • Never-withdraw cohort. VM-21 prescribes 0.20 non-qualified and 0.05 tax-qualified for GMWB contracts R1; the Academy cautions that a material never-utilize cohort may understate reserves and suggests reassigning it to very-late cohorts R5 REG-R67.

  • Withdrawal intensity. Base run std: 100% of GAWA once activated, matching the GAPV construction R1; the prescribed partial-withdrawal assumption is 90% of the guaranteed annual amount for lifetime GMWBs and 70% for non-lifetime GMWBs R1.

  • Bonus interaction. Any withdrawal in a Contract Year kills that year’s bonus S1, so utilization timing and benefit-base growth are coupled; a utilization model that ignores the forfeiture will systematically mis-time activation.

Other behavior#

  • Excess withdrawals are not modeled in the base run std; the algebra is implemented and exercised by a switch, since the Academy notes GLB utilization is inefficient “at both ends of the spectrum” — taking less than the maximum and taking excess withdrawals R5.

  • Charge-increase opt-out. At each fifth Contract Anniversary the base run assumes the insurer does not increase the charge and the owner does not opt out std; opting out forfeits bonus, step-up and GWB Adjustment and blocks future premium S1, so a rational opt-out model is a joint decision, not an independent lapse-style rate.

  • Annuitization. 0% at all projection intervals for contracts without a GMIB, per the prescribed assumption R1; the representative contract has no GMIB.

Worked example — one month, two subaccounts, charge stack, GMDB claim test#

Anchor cell: male, issue age 60, single Designated Life, non-qualified; single premium $100,000 at issue with premium tax 0.00% std; allocation 60/40 std; Flex GMWB Single Core (phi_G = 1.25%, b = 6.00%, annual CV step-up, s = 105%) S3 and Roll-up GMDB (phi_D = 0.90%, ρ = 6.00%) S3; m + α = 1.30% S2; e_1 = 0.95%, e_2 = 0.65% std. No withdrawals to date.

Carried state at the beginning of month 27 (contract year 3; month 27 is the 9th Contract Quarterly Anniversary). The guarantee bases follow from the anniversary events: GWB = 100,000 → +6,000 bonus at anniversary 1 = 106,000 (contract value 104,000 std illustrative, below GWB, so no step-up) → +6,000 bonus at anniversary 2 = 112,000, then stepped up to the anniversary contract value of 112,500 [std illustrative], which sets BB = 112,500 and restarts the Bonus Period S1. RB = 100,000 × 1.06² = 112,360 S1 S3. NP = RP = 100,000. Scenario month: r_1 = +1.20%, r_2 = −0.30% std.

Step

Item

SA₁ (equity)

SA₂ (bond)

Total AV

1

BOM balances

66,000.00

44,000.00

110,000.00

2–3

No premium, no withdrawal

—

—

110,000.00

4

Growth factors: SA₁ 1.0120 × (1 − 0.0095/12) × (1 − 0.0130/12) = 1.0101034; SA₂ 0.9970 × (1 − 0.0065/12) × (1 − 0.0130/12) = 0.9953805

66,666.82

43,796.74

110,463.56

5

Rider fees at the quarterly anniversary: GLWB (0.0125/4) × GWB 112,500.00 = 351.56; GMDB (0.0090/4) × RB 112,360.00 = 252.81; total 604.37 cancelled pro rata (w₁ = 0.603519, w₂ = 0.396481)

−364.75

−239.62

−604.37

6

Annual contract fee: not an anniversary month; and AV ≥ $50,000 so it would be waived S2

—

—

0.00

—

EOM balances

66,302.07

43,557.12

109,859.19

—

Memo: M&E + admin collected inside unit value = (66,000 × 1.0111988 + 44,000 × 0.9964600) × 0.0130/12 = 72.30 + 47.50

—

—

119.80

—

Memo: fund expense collected by the funds (not insurer revenue) = 52.88 + 23.76

—

—

76.64

—

Memo: insurer charge income this month = 604.37 + 119.80

—

—

724.17

—

GMDB test: DB = max(AV 109,859.19, NP 100,000.00, RB 112,360.00) = 112,360.00; guarantee claim = 112,360.00 − 109,859.19 = 2,500.81; gross claim outflow = 112,360.00

—

—

—

—

Memo: in-the-moneyness M_G = 112,500.00 / 109,859.19 = 1.0240, M_D = 1.0228; λ = min[1, max(0.5, 1 − 1.25(1.0240 − 1.10))] = 1.000 R1 → no lapse suppression; base annual surrender 4.0% (in the CDSC period) R1 → monthly 0.3396% std conversion

—

—

—

—

Memo: CDSC if surrendered now — completed years since premium receipt = 2 → 6.5% band S2; earnings = 9,859.19, so the charge-free amount is 10% × RP = 10,000.00 S1

—

—

—

—

Memo: GAWA% is not yet fixed; a first withdrawal now at attained age 62 would fix g = 4.00% (band 60–64, Core) S3 and set GAWA = 4.00% × 112,500.00 = 4,500.00

—

—

—

Trace check on step 5: 110,463.56 − 604.37 = 109,859.19 ✓. Note that the account fell $140.81 over the month while the guarantee bases did not move at all — the mechanical source of moneyness drift, and the reason the rider fee income rises as the account declines.

Valuation and reserve pointers#

This library projects gross liability cash flows. Reserve and capital layers consume them and are cited, not reproduced:

  • VM-21 — the statutory standard and, in its scope, CARVM itself: aggregate reserve = Stochastic Reserve (CTE70 of scenario reserves) + additional standard projection amount

    • any Alternative Methodology reserve, determined both pre- and post-reinsurance-ceded R1 REG-R35. Sections 9–12 carry hedging under a Clearly Defined Hedging Strategy, contract holder behavior, prudent-estimate mortality and contract-level allocation REG-R35. AG 43 is not superseded — through reference in AG 43 those requirements also reach contracts issued before January 1, 2017, and the populations may be aggregated R1 REG-R38.

  • AP&P Appendix A item A-250, and AG 33 — the formulaic layer, cited for what it does not contain. A-250 (variable annuities) has been read in full and carries no reserve method: a definition, a per-account asset-coverage floor and a delegation of the reserve to A-820, whose ¶15 is CARVM REG-R156 REG-R153. AG 33, also read in full, reaches “all annuity contracts subject to CARVM” carrying elective benefits but is displaced here by the product-specific instrument under its own precedence clause — a clause that names no guideline, so the AG 43 pairing is [std, derived] REG-R151. Neither item changes a number in this model; both are cited so that the formulaic layer under VM-21 is stated rather than assumed.

  • C-3 Phase II RBC — the same projection at CTE(98) per LR027, with TAR = pre-phase-in VM-21 reserve + C-3 amount, the C-3 amount then grossed up by 1 / (1 − enacted maximum federal corporate income tax rate) R3; VM-21 §§4.A–4.E and the RBC requirements are identical apart from the elective federal income tax treatment REG-R35, so one projection serves both. The older C-3 Phase II instructions package still prints the pre-reform CTE 90 TAR and a 35% tax rate REG-R47 — structure only; the current level is CTE(98) R3 R4.

  • VM-22 / VM-V §1 — where the post-depletion GLWB payment stream lands: fixed income streams from guaranteed living benefits after account exhaustion are named in VM-22’s Reserving Categories and VM-V §1’s scope REG-R36 REG-R37. VM-22 does not cover the variable contract itself.

  • Tax reserve — IRC §807: the greater of net surrender value and 92.81% of the NAIC-prescribed method (CARVM, i.e. VM-21), capped at statutory REG-R16; the LB&I examination directive on AG 43/VM-21 tax reserves is unverified (irs.gov 404) REG-R72.

  • U.S. GAAP — the GLWB and GMDB are the paradigm market risk benefits at fair value through earnings under LDTI [REG-R34 — unverified, ASU 2018-12 not fetched (fasb.org 403); summary-based](#uslib-reg-r34), with ASOP No. 10 as the professional counterpart, which was retrieved and supplies the MRB definition and classification test REG-R71.

  • Standards for the modeling work — ASOP Nos. 7 REG-R27, 22 REG-R29, 56 REG-R32, 2 (non-guaranteed elements, expressly covering variable deferred annuities, so governing the rider-charge reset) REG-R26 and 54 REG-R70. There is no ASOP for VM-21: ASOP No. 52 is scoped to VM-20 life products, so any claim that it governs VM-21 is unverified and, on the retrieved ASB text, wrong R11 R12 REG-R31. The nearest guidance is the Academy’s non-binding VM-21 practice note supplement, whose eight sections (Transition, Standard Projection, Asset Modeling & Discount Rates, Scenarios, Hedging, C-3 Phase 2 RBC, Disclosures, Miscellaneous) map onto the decisions this model must make R4 REG-R66.

Key sensitivities and model risks#

Dominant assumptions, in order of impact on guarantee cost.

  1. Dynamic lapse on moneyness — the single most important behavioral assumption, since it determines how many deeply in-the-money contracts persist to become claims. The multiplier bounds [0.5, 1.0] and Table 6.3’s implied 84% suppression R1 span the plausible range; test both.

  2. GLWB utilization — timing first, intensity second. Activation age drives the GAWA% locked in S3, the number of bonus years earned S1 and the discount period. The never-withdraw cohort weight (0.20 non-qualified R1) is a direct multiplier on guarantee cost, and the Academy’s warning that it may understate reserves R5 is a live model risk, not boilerplate.

  3. Equity return distribution, not just its mean. Step-up plus bonus makes the benefit base convex: markets up ratchet the guarantee permanently and restart the 10-year Bonus Period S1; markets down leave it intact and raise the fee base. Volatility is worth more than drift here.

  4. The bonus/step-up ordering std — it moves the benefit base by a full year’s bonus in every ratcheting year.

  5. Rider fee reset. A five-yearly discretionary +0.25% step with a forfeiting opt-out S1 behaves nothing like a quarterly VIX²-driven rate inside a [0.60%, 2.50%] corridor S4.

  6. Post-depletion longevity. Once the account is exhausted the liability is a pure life-contingent annuity at GAWA S1; the 2012 IAM Basic/Scale G2 basis and its A/E deviation REG-R59 REG-R61 become the whole story.

Known modeling pitfalls.

  • Gross vs net death claim. Project DB(t) as the outflow and derive max(0, guarantee − AV) as the general-account strain — never the reverse, never both (see products/variable_ul/technical-notes.md).

  • The fee stops at AV = 0 S4. Accruing rider income after depletion systematically flatters the CTE70 tail.

  • Withdrawals are measured gross of charges for every guarantee calculation S1; using net proceeds understates the benefit-base reduction.

  • Excess-withdrawal ordering. The non-excess portion reduces the base dollar-for-dollar first, and the proportional factor for the excess is computed against the contract value after that reduction S1. Reversing the order changes both GWB and GAWA.

  • Any withdrawal kills the year’s bonus — including automatic withdrawals and RMDs S1; pro-rating the bonus for partial-year withdrawals is wrong.

  • The Bonus Period restarts on a Bonus-Base-increasing step-up up to the anniversary following age 80 S1. A hard-coded 10-year window from issue materially understates the guarantee in rising markets.

  • GMDB withdrawal adjustments are applied at Contract Year end, not at the withdrawal S1; applying them immediately changes the base the roll-up compounds on.

  • Growth cutoffs are age-based, not duration-based — roll-up and ratchet growth stop at the anniversary preceding the oldest Covered Life’s 81st birthday S1, so an issue-age-60 cell gets 20 roll-up credits and an issue-age-75 cell gets 5.

  • Charge-base confusion. M&E and admin are on account value, the rider fees on benefit bases, the contract fee per contract, the CDSC on Remaining Premium. Four bases in one stack; putting the rider fee on account value is the most common and most consequential error.

  • Fixed account and MVA are absent by design — the Roll-up GMDB election removes Fixed Account Options S1. If a variant re-enables them, note that no closed-form MVA factor was found in any of the four prospectuses read: Jackson discloses a rate-differential rule with a 0.25% dead band and a Fixed Account Minimum Value floor S1, so any algebraic MVA formula in a model would be unverified S1 — and that flag stays, because the contract formula itself was never disclosed in closed form. What has changed is that the absence is now explained rather than merely recorded: A-255, the AP&P Appendix A item for modified guaranteed annuities, requires the separate account liability to be at least the surrender value produced by the contract’s own market-value-adjustment formula and prints neither a formula nor a parameter for one REG-R157. No MVA formula is prescribed in the appendix at all, so a model’s MVA algebra can only ever come from the contract. A-255 ¶1’s four-element definition — deferred annuity, individual or group; assets in a separate account; values guaranteed if held for specified periods; nonforfeiture values on an MVA formula if held for shorter periods, with the assets in a separate account “during the period or periods when the contract holder can surrender the contract” — is also the test VM-21 §2.A.2 uses to exclude contracts falling under VM-A item A-255, so such a variant faces a scope question before it faces a formula question; that exclusion is VM-21’s text, not A-255’s REG-R157 REG-R35.

  • Rate-sheet vintage. Every current parameter above is dated 2026-04-27 S3; historical tables show bonus percentages moving 5/6/7% → 4/5/6% → 5/6/7% and the GWB Adjustment 200% → 105% within six years S1. An in-force model must carry the vintage.

  • Discretization drift. Monthly unit-value compounding of a daily charge S2, annual crediting of roll-up and bonus S1 and quarterly fee assessment S1 are three different clocks; changing any one changes the answer. Document all three.