The WOL_UK_S Model

Reference liability cash flow model for UK whole of life assurance.

WOL_UK_S is the executable counterpart of products/whole_of_life/technical-notes.md in the lifelib-products library. It projects gross best-estimate liability cash flows for single-policy model points of the two cells those notes specify, which share one engine:

RefWOL-UW — underwritten guaranteed whole of life. Full underwriting, guaranteed level premiums payable for life, the sum assured paid once on death or earlier terminal illness, suicide inside twelve months refunding premiums instead.

RefWOL-O50 — over-50s guaranteed acceptance. No underwriting at all, a fixed cash sum, a twelve-month moratorium during which non-accidental death returns the premiums paid rather than the cash sum, premiums ceasing at the anniversary on or after the 90th birthday while cover continues, and a crossover past which cumulative premiums exceed the cash sum.

Neither cell has an account value, a unit fund or a surrender value. Both are pure decrement protection models: premiums in, death benefits and expenses out, weighted by survivorship. That is the deliberate contrast with WholeLife_US_A, the U.S. whole life model in the same library, which is built around a guaranteed cash value schedule, three-factor dividends, paid-up additions and policy loans. None of that machinery exists here, and a lapse on either UK cell pays exactly nothing.

The arithmetic consequence is the product’s defining economics: every lapse extinguishes a liability for nothing. The FCA records that without the continuing-payer cross-subsidy insurers would need to rely on lapses to remain profitable, so the best estimate falls as assumed lapses rise — which makes lapse the assumption to govern hardest, and makes one plan’s pro-rata paid-up value variant [S9], which converts late lapses into paid-up liabilities instead of forfeitures, a different product rather than a small adjustment.

Spaces. The model contains two:

Data

Reads the three 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. Policy month t runs 1, 2, …, proj_len(), where proj_len() = 12 x (omega_age - entry_age): whole of life has no maturity, so the projection is truncated at a limiting age rather than ending at a contractual date. Premiums and expenses fall at the beginning of the month; deaths at the end, against the beginning-of-month in-force; lapses at the end after deaths. Escalation steps at policy anniversaries. Age is age last birthday, unlike every other model in this library — the underwritten cell’s specimen defines entry age that way.

What is sourced and what is not. The contractual mechanics are sourced: the moratorium and its return-of-premiums benefit, accidental death paying the full cash sum from day one, premium cessation at 90 with cover continuing, the absence of any surrender value, the suicide clause, the escalation ratios and the pro-rata paid-up value formula. Every rate is a standardization. The CMI’s current tables are restricted to Authorised Users, so the two mortality bases shipped here are [std] proxies shaped like the tables the notes name, and no insurer publishes premium rate tables, so the premium is a model point input. This model is a mechanics demonstration, not a pricing or reserving result. Replace the basis with licensed tables and company experience first.

Verification. tests/test_whole_of_life_uk.py asserts the notes’ eleven-row worked example to the penny and the in-force column to five decimals, including the month-12/13 moratorium discontinuity and the month-167 crossover.

Example

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