Annuity Product Pricing Suite

M-070 is a pricing suite, not a single engine: a common harness across the annuity product family that composes four product models living under firmmodel/products/. Each model shares the same BaseProductModel contract (parameter schema, calculate() cash-flow projection, compute_profitability(), get_termsheet()) and the same composed calculation engines (Investment, Lapse, Expense, Benefits, Reserve, plus Stochastic/Mortality where the product needs them). The four members differ in their crediting and guarantee mechanics, which is exactly where annuity pricing risk lives.

Representative engine — IndexedAnnuityModel (P-003), RILA configuration. The snapshot below exercises this engine because it runs cleanly and deterministically and exhibits the suite's most distinctive mechanic: the embedded-derivative option budget. The engine projects monthly cohort cash flows (calculate() in firmmodel/products/indexed_annuity.py). Each month it accrues investment income on the general-account backing assets, accrues a monthly share of the embedded-option cost, deducts expenses and rider charges, applies lapse with a surrender-charge deterrent, and rolls the account value forward as AV(t+1) = av·(1 + credited_return) − fees − withdrawals (floored at zero). The credited return is the heart of pricing:

• Upside is capped: credited = min(index_return · participation, cap).
• Downside under RILA is buffered: a loss within the buffer credits 0%; a loss beyond the buffer passes through as −(loss − buffer).

The option budget is the spread the general account can afford to spend on hedging the crediting promise: option_budget = portfolio_yield − expense_rate − profit_margin_target − option_budget_spread (_calculate_option_budget()), floored at zero — in the canonical run, 5% − 0.30% − 0.75% − 0.25% = 3.70% annual. The cost of the promise is computed by _price_index_option() via Black-Scholes option replication: the RILA crediting feature is decomposed into a long call spread (ATM call minus a call struck at the cap, scaled by participation — the capped upside) plus, for the buffer, a short put spread (ATM put minus a put struck at 1 − buffer — the cost of absorbing the first N% of loss). The FIA variant prices the call spread only (0% floor). The embedded-derivative fair value carried on the balance sheet is av · option_cost_pct · term_remaining_fraction, so it amortises to zero across the crediting term and resets each cycle. compute_profitability() discounts monthly net profit to a PVFP, profit margin, simple IRR, and return-on-capital.

The other three suite members (summarised):

• SpreadLiabilityModel (MYGA / fixed annuity / funding agreement / GIC, insmodel.L4.spread_liability) — pure ALM. The insurer earns portfolio_yield, credits a contractual credited_rate, and books the difference as net spread. No embedded derivative, no separate account.
• RILAModel (P-002, insmodel.L4.rila_model) — the earlier indexed-annuity model. Same call-spread/put-spread core as P-003 but without the unified RILA/FIA handling and option-budget abstraction; P-003 is the comprehensive successor.
• VAGuaranteeModel (variable annuity, insmodel.L4.va_guarantee) — separate-account product with embedded guarantee riders (GMDB/GMWB/GMIB/GMAB). Each guarantee is priced as a put option on the separate-account value relative to a guarantee/benefit base, funded by M&E and rider fees. Dynamic lapse is the key sensitivity: in-the-money guarantees suppress lapse, raising guarantee cost.

The pricing suite is parameterised per product; the table lists the load-bearing assumptions for the representative RILA run.

Operational notes. The crediting cap, buffer, floor and participation are product-design assumptions (contractual, set at issue) rather than calibrated experience assumptions — pricing risk here is the risk that the option budget is mis-set relative to the true hedge cost, not assumption-estimation error. The option budget is deliberately conservative. Lapse is the only behavioural assumption that materially feeds back into cost for indexed products; for VA guarantees, dynamic (moneyness-dependent) lapse is first-order.

Deterministic single-cohort run of the suite's representative engine, IndexedAnnuityModel (P-003) in its RILA configuration — reproducible, requires no live firm data (python scripts/model_snapshots.py M-070 in InsModel; mechanics asserted by tests/test_indexed_annuity_e2e.py, 13 tests passing). The provider is a MagicMock.

Input: account value $1,000,000 · 15% cap · 10% buffer · 100% participation · 6-year term · ANNUAL_POINT_TO_POINT crediting · implied vol 18% · r 4% · q 1.5% · index return +8%. Row shown is month 12 (the first annual crediting event).

The embedded option cost (8.90% of notional over the 6-year term) decomposes into a 5.70 call-spread leg (the capped upside) and a 3.20 put-spread leg (the 10% buffer) — directly visible in the replicating portfolio. Note the option budget shown is a rate (3.70% p.a.), while option_cost_pct is a 6-year term cost; the engine amortises the latter monthly when comparing against budget. The PVFP and profit-margin figures are pricing diagnostics from compute_profitability(), not statutory reserves.

Captured 2026-06-04 · deterministic, no live data.

1. The suite is a harness, not a single validated engine. M-070 documents four distinct product models under one card per the §12.3 "intended use" collapse (Q-03 remains an open collapse-vs-split debate). The snapshot exercises only IndexedAnnuityModel (RILA); the spread and VA-guarantee engines are summarised but not independently snapshotted here.
2. Deterministic index path in the standalone pricing run. calculate() projects on a single expected index return (8%); the capped/buffered payoff is path-dependent and asymmetric, so a single point estimate understates the true distributional cost. Full stochastic pricing requires StochasticScenarioAdapter.
3. Black-Scholes option pricing uses flat vol and a single rate. _price_index_option() assumes constant implied volatility and a single risk-free rate with no skew/term-structure. Real RILA/FIA hedging trades against a vol surface; the replication is first-order.
4. Embedded-derivative FV is a simplified amortisation, not a re-priced mark. The carried FV is a linear amortisation of the issue-date option cost across the term, not a fresh Black-Scholes re-mark each period to current moneyness.
5. Profitability metrics are simplified. IRR is a total_profit / AV / years approximation rather than a true cash-flow IRR solve; return-on-capital uses a flat 8% capital charge for all indexed products.
6. RILAModel (P-002) is partly superseded. It overlaps IndexedAnnuityModel (P-003); its IndexedProductEngine dependency is noted as stubbed in source. Carrying both is a known redundancy.
7. No live firm-data path (BV-032). All figures are from documented canonical inputs and MagicMock providers; reserve/MRB figures shown are pricing-harness outputs, not statutory or LDTI-reported values.

Tracked for ratification (not applied in this documentation pass). The following are output-changing / modeling-code items left for ratification, noted here for transparency: produce the Tier-1 validation-evidence pack (backtesting per MRM §10.2 + a sensitivity suite across the material assumptions); independently snapshot/validate the two non-snapshotted members (SpreadLiabilityModel, VAGuaranteeModel), not just the representative RILA run; complete 2L independent effective challenge and close RAT-070-v1.0.0 per MRM §10.6 (peer_review.status pending → signed); and resolve the embedded-derivative FV methodology (linear amortisation of issue-date option cost / flat-vol single-rate Black-Scholes vs a fresh re-mark to current moneyness). No model outputs, back-test numbers, or validation results were fabricated or changed in this pass.

Engine source: - ecosystem/InsModel/Models/firmmodel/products/indexed_annuity.py — IndexedAnnuityModel (P-003), representative engine. - firmmodel/products/spread_model.py — SpreadLiabilityModel; firmmodel/products/rila_model.py — RILAModel (P-002); firmmodel/products/va_guarantee_model.py — VAGuaranteeModel; firmmodel/products/base_product.py — shared contract; firmmodel/products/stochastic_adapter.py.

Tests: tests/test_indexed_annuity_e2e.py (13), tests/test_va_guarantee_model.py. Snapshot: scripts/model_snapshots.py M-070.

Standards: - ASOP No. 56 — Modeling. - FASB ASU 2018-12 (LDTI) — Market Risk Benefit (MRB) measurement for VA guarantee embedded derivatives. - ASOP No. 22 — cash-flow-testing context for annuity reserve seeding.

Internal: M-001 for engine-card depth exemplar; BV-032 (firm-data divergence); Q-03 (collapse-vs-split for the annuity family).

Card change history. Code-side change history lives in git log of the component files.

• 2026-05-08 — stub created from registry data per Decision 023 Phase 5 / B-07.
• 2026-06-04 — Tier-1 hand-authoring of Methodology, Key Assumptions and Their Justification, Output Snapshot (deterministic RILA run via scripts/model_snapshots.py M-070), Limitations, Validation Packet, and References from indexed_annuity.py + IndexedAnnuityModel legacy_metadata; stub marker advanced to ``.
• 2026-06-06 (RAT-070-v1.0.0 remediation, 1L) — assembled the Tier-1 validation-evidence pack at validation_evidence/M-070/v1.0.0/README.md (98 passing InsModel tests + deterministic snapshot reproducing this card's Output Snapshot + PRU disclosed-block bounds cross-check; honest gaps carried) closing COND-001; authored the per-version change log at M-070-changes.md closing COND-002; reconciled registry documentation_pack flags (validation_evidence/change_log → present); refreshed the Validation Packet rows to point at the pack/log. No model outputs, back-test numbers, or validation results were fabricated (Decision 053 §4).
• 2026-06-06 — documentation-pack completion pass: added a dedicated Standards Coverage section (ASOP 56 / ASOP 22 / ASU 2018-12 LDTI, each tied to applicability) with a frontmatter-vs-References reconciliation note and an asc_944-tag flag raised to engine-governance (no reg tag silently added); expanded Dependencies with the MRM §10.5(8) shared-component aggregate-risk view (benefit_engine shared with M-001/M-002/M-071; projection_orchestrator shared with M-001/M-002/M-003/M-051/M-100, sourced from engine_registry.yaml model_membership); corrected the Validation Packet "Independent challenge (2L)" row from "per registry" to an honest pending state (RAT-070-v1.0.0 not closed, peer_review.status = pending, revalidation due 2026-08-23, validation_evidence not produced) and added a backtest/sensitivity-evidence "pending" row; noted gated/ratification items under Limitations. No model outputs, back-test numbers, or validation results were fabricated or changed.