The ULSG_US_S Model#

Reference liability cash flow model for U.S. guaranteed universal life (ULSG).

ULSG_US_S is the executable counterpart of products/guaranteed_ul/technical-notes.md in the lifelib-products library. It projects gross liability cash flows for a single-life, flexible-premium universal life policy with a single shadow-account secondary guarantee (AG 38 8E Policy Design #1 [R1]; VM-01 shadow-account definition [R2]): level death benefit only, a notional guarantee account with its own load, charges and credited rate, an in-force test SG - L > 0 that keeps the contract alive after the real account value is exhausted, a built-in return-of-premium endorsement at anniversaries 20 and 25 [S1], a 15-year surrender charge, and no maturity date – charges and premiums cease at attained age 121 and coverage continues [S7].

The product is built on the universal life chassis. Its technical notes say so explicitly, and this model follows UL_US_S in structure, naming and processing order, deviating only where the guaranteed-UL notes restate a recursion with their own parameters. The two documented deviations are that the account value for the net amount at risk is measured after the expense charges and before the cost of insurance (the UL chassis measures it before the entire monthly deduction), and that the guaranteed-UL notes’ CSV_t already nets policy debt, which is the chassis’ ncsv_pp.

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-policy 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 policy. In Data they are evaluated once, however many policies 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 on policy monthiversaries. t counts policy months from the start of the projection, 1-based: t = 1 is the issue month of a new-business model point and the first projected month of an in-force cell, which sits duration_mth_init() completed policy months after issue. The technical notes index the same months by their absolute policy month number, starting at duration_months + 1; the worked example’s months 301-305 are therefore t = 1 to t = 5 here, with duration_mth(t) = 300 + t - 1. State variables the notes define at t = 0 – AV_0, SG_0, L_0, CumPrem_0, l_0 = 1, g_0 = 0 – are the t == 0 branch of the corresponding recursion.

proj_len() = 12 * (121 - age_at_entry()) - duration_mth_init(), the notes’ maximum projection length: the projection runs to attained age 121, where charges and premiums cease. Coverage continues past that point in the contract [S7]; the illustrative mortality table reaches 1.0 at attained age 120, so nothing survives the horizon and pols_maturity(t) is identically zero – guaranteed UL has no maturity date.

Within each month the notes’ monthiversary order is followed exactly. At the beginning of the month (BOM): the status check, premium and its two loads (one to the account value, one to the shadow account), withdrawal and its fee, the expense charges, the death benefit and corridor test, the net amount at risk on both accounts, the cost of insurance on both, and the insufficiency test that decides between a forgone deduction and the grace period. At the end of the month (EOM): interest on both accounts and loan interest accrual, the in-force test, then the decrements – death, then surrender, then return-of-premium exercise. Premiums and expenses therefore fall at BOM and are weighted by pols_if(t); death claims by pols_if(t) * mort_rate_mth(t), surrenders by pols_if(t) * (1 - mort_rate_mth(t)) * lapse_rate_mth(t) and refunds by the same survivors times rop_rate(t).

Cash flows are undiscounted. Loads, charges, interest credits and every shadow-account entry are internal transfers, not external cash flows: they drive the account value, the surrender value and the in-force test only.

One documented deviation from the notes [std]. The notes floor the account value at zero only while the guarantee is active: their step 6 sets AV''_t = 0 in the guarantee branch and gives the grace branch no account-value recursion at all. This model applies the floor unconditionally – in the grace months and after a lapse as well – because a negative balance would break the account-value roll-forward, which closes on the deduction actually taken and nothing is taken from an exhausted account. No cash flow moves: a policy in grace surrenders for nothing by construction, and pols_if(t) is zero once it has lapsed. What it does mean is that the per-policy account-value and forgone-deduction cells keep running after the policy has gone, and that mth_deduction_forgone(t) is the guarantee’s running cost only while is_guar_supported(t) holds – in grace the same figure is the notes’ required grace payment instead. The README says so, and a test pins it.

What is sourced and what is not. The contractual elements come from the product specification’s composite of retrieved carrier documents: the 25% premium load and the $5.50 monthly per-policy charge [S3][S7], the 2.0% guaranteed credited rate [S3][S5][S7], the 5.0%/3.0% loan rates [S4], the 61-day grace period [S7], the return-of-premium percentages, anniversaries and 40%-of-face cap [S1], the in-force test on the shadow account net of indebtedness [S4][S2][S9], and the cessation of charges at attained age 121 [S7]. Every shadow-account parameter is a standardization – no carrier publishes them and no specimen policy form was retrieved – as are the $0.20 and $0.05 per-unit charges, the 65% current-to-guaranteed COI factor, the 3.5% current credited rate, the 15-year $18 per $1,000 surrender charge, the mortality and lapse tables, the mortality improvement scale, the dynamic lapse formulas, the return-of-premium exercise rates, the premium persistency probability and every expense. The illustrative guaranteed maximum COI curve shipped in coi_rates.csv is not the 2017 CSO table, which is licensed and may not be reproduced here; it is a Perks curve fitted to the two figures the technical notes state – 8.615 per $1,000 per month at attained age 85, and a solved level lifetime no-lapse premium near $10,800 for the anchor cell. 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. Modules the technical notes describe but do not specify completely enough to project, or that belong to a different layer, all named here and in the README so their absence is not mistaken for an oversight:

  • The cumulative-premium-test guarantee design (AG 38 8E Design #2). The notes document it as a swap of SG_t for the pair (CumPrem^net, ReqPrem), but give no required-premium schedule, so there is nothing to project.

  • Catch-up premium payment. The catch-up requirement C_t is a complete formula and is implemented as the diagnostic catch_up_prem_pp(); the notes state expressly that catch-up behaviour is not modelled in the base run, so no catch-up premium is ever paid and no guarantee is ever restored.

  • Grace cure. The required cure payment is implemented as cure_premium_pp(), but the notes give no cure probability, so a policy that enters grace always lapses when the 61 days expire.

  • New policy loans, repayments and withdrawal utilisation. The mechanics are implemented – loan interest accrual, the loaned/unloaned interest split, the dollar-for-dollar shadow reduction, the $25 fee – but the notes set utilisation to zero in the base model point and give no pattern, so loan_bal_pp(t) only rolls an opening balance forward and wd_pp comes from the model point table.

  • 7702 / 7702A testing. Guideline premium limits and MEC status are flagged by the notes as out of model; they cap or classify premiums and generate no insurer cash flow, and no guideline premium inputs are given for this product.

  • Terminal illness acceleration, treated as cash-flow-neutral by the notes; selective-lapse mortality adjustment, which the notes exclude expressly; and non-guaranteed-element re-rating, which is out of scope.

  • Reserves. Like the rest of this library the model stops at gross liability cash flows; VM-20 ULSG, AG 38 and A-830 consume them and are cited, not reproduced.

The funding-premium solve is implemented, because the notes give the complete algorithm: no_lapse_premium() bisects guar_min_sg() over the level annual premium with decrements off, on the notes’ own domain. It is a side calculation; nothing in the projection depends on it.

Model points. model_point_table.csv carries four points, all on the anchor cell male 60 ANB / NT Standard / $500,000, because the illustrative COI table covers that cell alone. Point 1 is the technical notes’ worked-example model point: an in-force cell at 300 completed policy months with an account value of $2,400, a shadow account of $118,000 and a level $10,800 annual premium. Point 2 is the same policy from issue, which is the base behavioural run and the cell whose solved no-lapse premium the tests check. Point 3 funds the same lifetime guarantee with a single premium, exercising the single-pay lapse multiplier. Point 4 elects a guarantee to age 90 and underfunds it, so the shadow account runs out, the catch-up requirement becomes positive, the grace period opens and the policy lapses for insufficiency – the one path the other three never take. A model point on any other issue age, sex or class requires coi_rates.csv to be extended first; a test asserts every model point in the table actually projects.

Verification. Model point 1 is the anchor of the worked example in the technical notes, and tests/test_guaranteed_ul_us.py asserts every cell of all five of its rows – premium, net premium to each account, the monthly deductions on each account, the interest credited to each, both closing balances, the forgone deduction and the status – together with the notes’ NAAR constants, the exhaustion of the account value in month 304 and the guarantee carrying the contract from month 305.

Example

>>> import modelx as mx
>>> model = mx.read_model("products/guaranteed_ul/ULSG_US_S")
>>> model.Projection[1].result_av()