The MYGA_US_S Model

Reference liability cash flow model for U.S. fixed deferred annuities (MYGA).

MYGA_US_S is the executable counterpart of products/fixed_deferred_annuity/technical-notes.md in the lifelib-products library. It projects gross liability cash flows for a single-contract model point of a single-premium, book-value multi-year guaranteed annuity: one purchase payment credited in full, an insurer-declared effective annual rate guaranteed for a five-year period, a declining surrender charge, a 10% annual free-withdrawal allowance, a two-sided market value adjustment, and underneath all of it the NAIC Model #805 minimum guaranteed surrender value.

This is the deferred annuity base chassis of the library. The fixed-indexed annuity, variable annuity and registered index-linked annuity notes reference the surrender benefit composition order and the Model #805 floor construction specified here.

Spaces. The model contains two:

Data

Reads the seven 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 policy months, t = 1, 2, ..., proj_len(), and the contract year is policy_year(t) = ceil(t / 12), so anniversaries fall at t = 12, 24, .... Note the contrast with Term_US_A, where t counts years: monthly is the coarsest grid that hits every contract anniversary exactly while still resolving the guarantee-period-end window and the shock-lapse boundary to within one step [std].

The month’s processing order follows the technical notes exactly. At the beginning of the month (BOM): roll the free-withdrawal counters; apply the guarantee-period boundary (the 30-day window, the rate redeclaration and, under rollover, a fresh surrender charge and MVA schedule); take the elective withdrawal, giving av_pp_at(t, "BEF_INV"); take annuitization elections — valued on that same pre-crediting account value, because the notes place the election at BOM while naming the post-crediting SV(t) for the transfer, and the two cannot both hold on a monthly grid [std]; update the IRC 72 tax basis. At the end of the month (EOM): credit interest, giving av_pp(t); roll the Model #805 floor mgsv_pp(t); and apply decrements in the order annuitization, mortality, surrender [std], with every decrement benefit valued on the post-crediting account value.

t = 0 is the issue instant. The single premium, the acquisition commission and the premium tax all fall there, as they do in the notes’ cash flow ledger, and av_pp(0), mgsv_pp(0) and pols_if(0) are the initial branches of the three recursions. result_cf() therefore starts at t = 0, not at t = 1.

pols_if(t) is the count in force at the start of month t, the library-wide convention (pols_if(1) == pols_if_init(), as in Term_US_A), and it is the weight applied to that same month’s cash flows, so the pols_if column of result_cf() reconciles with the row it sits on. The technical notes’ end-of-month l(t) is unchanged and is read as pols_if_at(t, "AFT_DECR"). Likewise lapse_rate(t) is the annual total surrender rate and lapse_rate_mth(t) the monthly one, pairing as mort_rate / mort_rate_mth do.

proj_len() is 12 * (maturity_age - age_at_entry()) months, running to the contract anniversary at attained age 100 [std] — the last attained age in the sourced cap band on the renewal surrender charge, tabulated as 4% at 94 down to 0% at 98-100 [S1][S2]. The cap reaches zero at 98; 100 is where the sourced band stops, which is why it is the horizon. The technical notes state no projection horizon; the choice is the model’s, and the survivors at that point are annuitized out through pols_maturity() so the in-force roll-forward closes.

Undiscounted. Like every model in this library, this one projects gross liability cash flows only. Reserves and discounting are a separate layer; the notes’ Valuation and reserve pointers section cites VM-22, A-820/AG 33 and IRC 807 rather than reproducing them. The contractual discounting that lives inside a benefit formula — the geometric MVA factor — is part of the product and stays.

What is sourced and what is not. The contractual elements come from the composite specimen: the 4.45% initial declared rate, the 0.25% GMIR and the 2.80% GMSV rate [S11]; the 9/8/7/6/5 initial surrender charge schedule and the 10% free-withdrawal allowance [S10]; the 5/4/3/2/1 renewal schedule and its attained-age cap [S1][S2]; the linear duration MVA and its application base [S8][S9]; the symmetric cap at the surrender charge [S2]; the 30-day guarantee-period-end window [S1][S2][S5][S6]; the death benefit at full account value [S1][S2][S13]; and the Model #805 construction — 87.5% of gross consideration accumulated at the contract GMSV rate, with the indexed statutory rate floored at 15 basis points, not 1% [R1 4.A, 4.B]. The prescribed base lapse table and the dynamic lapse functional form are VM-22 [R2 6.B.5].

Everything behavioural and expense-related is a standardization: the mapping of VM-22 Table 6.5 onto a five-year architecture, the 1.0% annuitization take-up at each window, the 0% partial withdrawal base run, the 2.00% acquisition commission, the $50 per contract per year maintenance expense inflating at 2.5%, the 0% premium tax, the 0.35 best-estimate MVA factor on dynamic lapse, the exogenous reference-yield and competitor-rate scenarios, the illustrative mortality table, and the attained age 100 projection 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 RMD module (the notes give the charge and MVA exemption but no RMD amount formula); the nursing-home and terminal-illness waiver withdrawals (no incidence basis is given); the VM-22 Table 6.2 age-banded partial-withdrawal rates (the retrieved table is the Qualified column only and its 80-and-over row was truncated, and the notes say not to present it as a non-qualified assumption); the greatest_of free-withdrawal rule (the notes describe it but give no formula); the gross-up solve for a contract promising a stated net check (wd_pp is gross by construction); the Model #805 section 6 paid-up annuity leg (noted but not implemented in the notes themselves); and check_margin(), because the product carries no contract charges and the model projects no asset side, so the notes define no margin decomposition to check. check_av_roll_fwd() and check_pols_roll_fwd() are implemented — no argument, returning a bool over every projected month, with the signed per-month residual under check_av_roll_fwd_resid(t) / check_pols_roll_fwd_resid(t). Stochastic scenario generation is out of scope: the reference yield and competitor rate are read from a deterministic scenario table.

Model points. model_point_table.csv carries seven contracts on the same anchor cell — male 60 ANB, non-qualified, $100,000 single premium, 5-year guarantee period — that differ only in the switches the technical notes make first-class parameters, because the cross-carrier divergence in those switches is the notes’ own headline finding. Point 1 is the worked example anchor; point 2 repeats it under the stress reference yield that forces the symmetric cap and the nonforfeiture floor to bind; points 3 to 7 carry the Camp B annual-redeclaration architecture, the registered-contract conventions, the Midland conventions, the asymmetric cap and the declared-differential MVA. Between them they exercise all three MVA families, all five cap rules, both renewal architectures, both Model #805 withdrawal conventions and both free-withdrawal rules, so no branch of the notes’ parameter set is dead code. A test asserts every point projects.

Verification. tests/test_fixed_deferred_annuity_us.py asserts every row and column of the notes’ worked example table (all seven months, money to the cent), both surrender traces line by line including the capped MVA and the binding Model #805 floor, the geometric branch factors from the Nationwide contract, the in-force and account value roll-forwards, and one test per entry in the notes’ Known modeling pitfalls list.

Example

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