The VA_US_S Model

Reference liability cash flow model for U.S. variable annuities with guarantees.

VA_US_S is the executable counterpart of products/variable_annuity/technical-notes.md in the lifelib-products library. It projects gross liability cash flows for a single-contract model point of an individual deferred variable annuity carrying two written options: a guaranteed lifetime withdrawal benefit (GLWB) tracked on a Guaranteed Withdrawal Balance that grows by a bonus and ratchets to contract value, and a guaranteed minimum death benefit (GMDB) tracked on a roll-up Benefit Base. Contract value follows separate-account fund performance with no insurer guarantee; both benefit bases are shadow accounts that never fall with the market.

Relation to the chassis. The deferred annuity chassis of this library is MYGA_US_S, and the naming, the Data/Projection split and the timing-argument vocabulary follow it. Its mechanics deliberately do not carry across, and the chassis notes say so in terms: a VA’s separate account is outside NAIC Model #805, which reaches a VA only through its fixed account under Model #250 §7.B [REG-R42][REG-R43] — and electing the Roll-up GMDB removes the Fixed Account Options altogether [S1]. There is therefore no minimum guaranteed surrender value, no market value adjustment and no declared credited rate in this model. What replaces them is a unit ledger, a four-base charge stack and two path-dependent guarantees.

Spaces. The model contains two:

Data

Reads the eight input CSVs and holds their filename References. It takes no parameters, so each file is read once per model.

Projection

The by-contract projection, parameterized by point_id: Projection[1] is an ItemSpace projecting model point 1. It reaches the input tables through its data Reference, which resolves to the single Data Space.

The split matters for more than tidiness. Because Projection is parameterized, every Projection[N] is a separate ItemSpace with its own cells cache; readers placed there would re-read every file for every model point. In Data they are evaluated once, however many contracts are projected.

Input data is external: CSVs in the model folder’s parent directory, read at run time rather than stored inside the model. The model folder itself holds no data, so the model and its inputs must travel together.

Projection basis. Monthly steps. t counts projection months, t = 1, 2, ..., proj_len(), with t = 0 the entry instant carrying the single premium and the initial branch of every recursion. The policy month is duration_mth(t) = duration_mth_init() + t; the two coincide for an at-issue cell and differ for an in-force cell, and every calendar test is written on duration_mth. policy_year(t) = ceil(duration_mth(t)/12), so Contract Anniversaries fall at the end of policy months 12, 24, … and Contract Quarterly Anniversaries at the end of policy months 3, 6, 9, … [std]. Note the contrast with Term_US_A, where t counts years: monthly is required here because the base contract charge accrues daily on separate-account value, the rider charges are assessed quarterly on benefit bases, and the roll-up and bonus are credited annually — three different clocks, and changing any one changes the answer.

Within a month: at the beginning of the month (BOM) the premium buys units at the prior unit value and raises GWB, BB, NP, RP, RB, GAWA and ADJ, then the withdrawal is taken — fixing the GAWA% if it is the first, splitting into excess and non-excess portions, charging the CDSC and updating GWB, GAWA and BB. Unit values then grow over the month. At the end of the month (EOM) the two rider fees are assessed at a Contract Quarterly Anniversary and the annual contract fee at a Contract Anniversary, both by pro-rata unit cancellation; then, at a Contract Anniversary only, the seven guarantee events in the notes’ order; then the depletion test; then decrements, death first, then surrender [std]. If the contract is already depleted the whole of that is skipped and the post-depletion GLWB payment routine runs instead.

proj_len() runs to attained age omega_age = 120 [std], the terminal age of the mortality table, because once the account is exhausted the For Life Guarantee is a pure life-contingent annuity at GAWA. The survivors at that horizon are carried out through pols_maturity() so the in-force roll-forward closes.

pols_if(t) is the count in force at the start of month t — the notes’ l(t-1) — and is the weight carried by every cash flow on that row, so the in-force column of result_cf() reconciles with the cash flows printed beside it. The notes’ own end-of-month l(t) is pols_if_at(t, "AFT_DECR"). Two other names follow the library rather than the notes: lapse_rate(t) is the annual surrender rate and lapse_rate_mth(t) the monthly one, matching mort_rate / mort_rate_mth; and the net premium credited to the account value is prem_to_av_pp(t), the per-contract form of prem_to_av(t).

Undiscounted. Like every model in this library, this one projects gross liability cash flows only. Reserves and discounting are a separate layer: the notes cite VM-21’s CTE70 stochastic reserve, C-3 Phase II’s CTE(98), VM-22/VM-V §1 for the post-depletion stream, IRC §807 and LDTI market risk benefits rather than reproducing any of them. Guarantee cost cannot be valued deterministically — VM-21 makes that structural, the Alternative Methodology being unavailable to any GLWB block [R1]. The base deterministic run implemented here verifies the recursion, not the value of the guarantees.

What is sourced and what is not. The contractual elements come from the composite specimen: the 1.30% base contract asset charge and the $35 contract fee waived at $50,000 [S2]; the 8.5%/7.5%/6.5%/5.5%/5.0%/4.0%/2.0%/0.0% withdrawal charge scale on Remaining Premium by completed years since receipt, and the 10%-of-Remaining-Premium free withdrawal with earnings out first [S1][S2]; the excess-withdrawal algebra — dollar-for-dollar then pro rata — and the GMDB withdrawal adjustment applied at Contract Year end [S1]; the $10,000,000 benefit base cap, the age-81 GMDB growth cutoff and the 59 1/2 For Life trigger [S1]; and the rate-sheet parameters dated 2026-04-27: GLWB charge 1.25%, GMDB charge 0.90%, bonus 6.00%, roll-up 6.00%/5.00%, GWB Adjustment 105% and the GAWA% grid [S2][S3]. The dynamic lapse multiplier, the base surrender table, the withdrawal-year factor, the zero surrender rate at AV = 0 and the prescribed maintenance expense are VM-21 [R1].

Everything else is a standardization: the monthly discretization of the daily asset charge and of the decrements; the quarterly anniversary calendar; the M&E/administrative split of the 1.30% total; the pro-rata deduction of the rider charges, extended from the cited contract-fee rule; the 3.00% guaranteed maximum GLWB charge; the bonus-then-step-up ordering; the 60/40 two-subaccount allocation and its fund expense ratios; the reverse-engineered illustrative return path; activation at age 70 at 100% of GAWA; the illustrative mortality table; the premium portion of a withdrawal for the Remaining Premium roll-forward; the contract-value base for the GMDB proportional adjustment; the reading that lets the basic GMDB election’s proportional withdrawal reduction bite against the notes’ unreduced NP floor — the two tables contradict each other and the elected form is taken to govern, which the README sets out in full; the capping of charges and withdrawals at the available account value; and the attained age 120 horizon. This model is a mechanics demonstration, not a pricing or reserving result. Replace the assumption tables with company data before drawing any conclusion from the output.

Not implemented. Named here so the gaps cannot be mistaken for oversights. The stochastic scenario interface — real-world and risk-neutral scenario sets, proxy fund mapping, and the CTE70/CTE(98) layers that consume them — is out of scope: returns come from a deterministic scenario table, and the notes are explicit that a deterministic run cannot value the guarantees. The Withdrawal Delay Cohort Method and the never-withdraw cohort (weights 0.20 non-qualified and 0.05 tax-qualified [R1]) need a revised-GAPV construction the notes do not supply, and would require blending parallel projections. The RMD module: L = max(GAWA, RMD) carries the RMD term but no divisor table is given and the base cell is non-qualified. The combination GMDB max(roll-up, ratchet) needs two parallel benefit bases and the notes state neither which component carries the charge nor how the withdrawal adjustment splits between them. The highest-quarterly step-up basis is implemented as the highest of the four most recent quarterly contract values, without the source’s adjustment of each for subsequent premiums and withdrawals. The two-table post-depletion payout [S8] has no Table B values in the sources. The Latest Income Date at owner age 95 [S2] is not a forced annuitization: the prescribed annuitization assumption is 0% at all projection intervals for a contract with no GMIB [R1], and no retrieved document carries an annuity rate table. Premium-tranche CDSC aging is absent: Remaining Premium is carried as one undifferentiated pool and the charge band is read off the contract duration, so a subsequent premium does not restart its own charge clock. The notes key the band on completed years since receipt of the premium being withdrawn [S2], which coincides with the contract duration only while the contract is single premium — model point 4 is not, and a test pins the divergence. The charge-increase opt-out, the terminal illness and extended care waivers, spousal continuation, joint-life elections and the transfer charge are all described in the sources and not modelled. And check_margin() is absent: the model projects no asset side, so there is no charge-versus-cost decomposition to check; check_av_roll_fwd(), check_pols_roll_fwd() and check_charge_split() are implemented and all three close to floating point. Each takes no argument and returns a bool covering every projected month, as savings.CashValue_SE does, with the signed per-month residual available as check_av_roll_fwd_resid(t) and its two counterparts for when one of them fails.

Model points. model_point_table.csv carries nine contracts on the same anchor cell — male 60 ANB, single Designated Life, non-qualified, $100,000 single premium, 60/40 allocation, Flex GMWB Single Core and Roll-up GMDB — that differ only in the switches the technical notes make first-class parameters. Point 1 is the worked-example anchor, projected from issue on a return path reverse-engineered so that the notes’ own carried state at the beginning of month 27 falls out of the projection exactly. Point 2 is the same carried state entered directly as an in-force cell, so the worked-example month reproduces without depending on that return path — the two readings agree to the cent and a test pins both. Point 3 runs a declining market to exhaustion and exercises depletion and the insurer-funded GLWB payment stream; point 4 the excess-withdrawal algebra and a subsequent premium; point 5 the highest-quarterly step-up basis and the annual-ratchet GMDB; point 6 the VIX-squared fee reset and the CMT-linked roll-up; point 7 a never-withdraw cell on the included proportional return-of-premium death benefit with no withdrawal charge, which is what exercises the GWB Adjustment Date and the five-yearly discretionary fee increase; point 8 a never-withdraw cell on the Roll-up GMDB, whose Benefit Base compounds cleanly to the age-81 cutoff with no withdrawal adjustment to muddy it and whose rider fees on the two bases eventually exhaust the account at policy month 555; and point 9 the same proportional return-of-premium death benefit as point 7 but withdrawing from age 70, which is what makes that form’s G <- G x (1 - W/AV_pre) reduction bite. A test asserts every point projects.

Verification. tests/test_variable_annuity_us.py asserts every row and column of the notes’ worked example: the two subaccount balances at each of the six printed steps, the two growth factors to seven decimals, the pro-rata weights to six, the two rider fees, the end-of-month balances, all three memo lines (M&E and admin inside the unit value, the fund expense that is not insurer revenue, and total insurer charge income), the GMDB test with its gross and net figures, the moneyness ratios and lapse multiplier, the CDSC and free-withdrawal memo, and the GAWA memo — on both the at-issue and the in-force reading of the anchor. It also asserts the carried state the notes narrate at anniversaries 1 and 2, both roll-forwards at every month, and one test per entry in the notes’ “Known modeling pitfalls” list.

Example

>>> import modelx as mx
>>> model = mx.read_model("products/variable_annuity/VA_US_S")
>>> model.Projection[1].result_cf()