The Term_UK_S Model

Reference liability cash flow model for UK guaranteed-premium term assurance.

Term_UK_S is the executable counterpart of products/term_assurance/technical-notes.md in the lifelib-products library. It projects gross best-estimate liability cash flows for a single-policy model point of UK term assurance in the three benefit shapes the representative product offers — level, decreasing at a client-selected schedule rate, and family income benefit — with terminal illness inside the death decrement, an optional RPI indexation option, and no tail states of any kind: cover ceases at the end of the term with no maturity value, no renewal and no conversion.

That last point is the structural difference from Term_US_S, the U.S. model in the same library. A U.S. level premium term policy jumps to ART rates at the end of the level period and runs on to attained age 95; a UK policy simply stops. There is no post-level-term phase, no shock lapse, no jump ratio and no mortality deterioration factor here, and importing them would materially misstate UK term liabilities.

Spaces. The model contains two:

Data

Reads the four 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. The time index t is 0-based and counts policy months from issue: t = 0 is the issue month, the policy year containing month t is t // 12 + 1, and the frame runs t = 0, 1, ..., proj_len() - 1, where proj_len() = term_mths() = 12 x policy_term() is the number of policy months; an in-force model point opens at t = 12 x duration_inforce(). Premiums, maintenance expense and renewal commission fall at the start of the month; death and terminal illness claims and their claim expense at the end; lapses act on the survivors of mortality, death before lapse. Acquisition expense and initial commission fall at issue, in t = 0.

The notes take an annual grid as their base and name a monthly one as the arbiter of its two approximations — the mid-year benefit balance of the decreasing shape and the annual-in-advance premium, which they call an offsetting pair. This model is that monthly grid, so neither approximation is here: the decreasing benefit is the exact schedule balance of the month the claim falls in, the premium is the contractual monthly one and stops the month the policy leaves, and family income benefit instalments are counted one by one rather than rounded to six in the year of death and twelve thereafter. premium_mode is live rather than inert — an annual payer is charged twelve months’ premium in the first month of each policy year — and the waiver rider’s 26-week deferred period is carried as six months between incidence and the first waived premium. The assumption tables stay in the annual units they are quoted in, converted month by month with 1 - (1 - r)^(1/12), the notes’ own convention.

What is sourced and what is not. The contractual mechanics are sourced: the decreasing-shape amortization, the family income benefit as an annuity-certain to the end of the term, terminal illness as a 100% acceleration rather than an extra benefit, the absence of any surrender value, and the indexation option’s cover and premium caps. Everything quantitative is a standardization introduced for the reference implementation. No UK insurer publishes premium rate tables — pricing is quote-driven, and only the £5/month minimum is public — and the current CMI “16” Series assured lives tables are subscriber-restricted, so both the premium and the mortality basis shipped here are constructed. This model is a mechanics demonstration, not a pricing or reserving result. Replace the assumption tables with company data, and the mortality basis with licensed tables, before drawing any conclusion from the output.

Model points. Eight, covering all three benefit shapes, both mortality bases, the indexation option, a joint first-death policy, waiver of premium, family income benefit commutation, and one policy already in force at duration 5. Model point 1 is the anchor cell of the worked example in the technical notes.

Verification. tests/test_term_assurance_uk.py asserts the notes’ worked-example rows and their policy-year totals to the penny and the in-force column to six decimals, the anniversary identity that ties pols_if(12y) to an annual-grid roll-forward of the same table, the B(60) = £134,588 decreasing-schedule anchor, and the family income benefit ledger against an independent rebuild.

Example

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