Funds-Withheld / Modco Reinsurance Embedded Derivative

Engine BUILT and code-grounded. insmodel.L4.funds_withheld_modco (FundsWithheldModcoEngine, firmmodel/engines/funds_withheld_modco_engine.py) is implemented, @engine-decorated, bound in engine_registry.yaml (model_membership: [M-041]), SR 11-7 legacy_metadata archived, with 11 unit tests passing and a reproducible deterministic snapshot. The method below describes the running code (Decision 049 doc-currency: this narrative matches the engine source).

The method is ASC 815-15 host-vs-embedded-derivative bifurcation. A funds-withheld / modco treaty is separated into its host (financing) leg — the withheld / modco reserve balance earning the contractual host_funding_rate, carried at amortised cost and reported as the residual host_carrying_value = withheld_balance − embedded_derivative_fv — and the embedded derivative: the feature that passes the total return of the withheld / modco asset portfolio to the counterparty. The embedded derivative is fair-valued as the present value of the excess-return leg over the projection horizon:

ED_fv = Σ_t  notional_t · (asset_total_return − host_funding_rate) · participation · DF(t)

where asset_total_return = risk_free_rate + asset_credit_spread (OAS decomposition), notional_t = withheld_balance · (1 − balance_runoff)^(t−1), DF(t) discounts at the flat per-treaty discount_rate, and an optional contractual floor on the passed return is supported. The credit-spread-sensitive, net-income-volatility-driving portion is isolated as ed_credit_spread_value (the leg repriced with OAS set to zero, differenced), and a +1bp OAS sensitivity is reported as ed_credit_spread_dv01 so downstream stress suites can shock the embedded derivative without a full re-projection. No firm calibration is invented — every economic input (withheld balance, host funding rate, OAS, discount rate, participation) is supplied via engine_context.

This engine does not replace insmodel.L4.reinsurance_engine (ReinsuranceEngine, firmmodel/engines/reinsurance_engine.py), which handles only modco cash-flow mechanics (_apply_modco: modco_adjustment = ceded_reserve_change + interest_on_ceded). That engine does not bifurcate the contract and does not fair-value the total-return feature — exactly the step this engine adds.

Engine ships UNCALIBRATED — no A-NNN assumptions are bound. The registry entry lists assumptions: [], and the engine carries no @uses_assumptions decorator: every economic input is a treaty input supplied at runtime via engine_context, not a registered calibrated assumption. This is a deliberate design choice (the same posture as ReinsuranceEngine) — the engine implements the deterministic ASC 815-15 bifurcation math and never invents firm calibrations.

The method exercises the following input families, each supplied per treaty (not a registered A-NNN value):

• Asset credit spread (OAS) — the option-adjusted spread of the withheld / modco portfolio; the credit-spread-sensitive driver of the total-return feature. Supplied as asset_credit_spread.
• Discount basis — the flat per-treaty discount_rate for the excess-return leg (defaults to the host funding rate).
• Total-return participation — participation_rate (default 1.0 = full pass-through; per-treaty override for partial-participation structures).
• Projection horizon — projection_years (default 10).

If firm-calibrated defaults are later registered as A-NNN assumptions (e.g. an OAS-decomposition basis sourced from a credit-spread feed), that binding plus the matching @uses_assumptions decorator is a ratification item — see Limitations. It is not claimed here today (no such assumptions exist on assumption_domains.yaml).

Deterministic snapshot — reproducible, no live data. Models/scripts/model_snapshots.py M-041 reproduces the table below on documented synthetic canonical treaties (BV-032-immune; no FRED / firm data touched). No firm withheld balance, OAS, funding rate, or disclosed embedded-derivative balance is asserted.

The FWH001 case is hand-verifiable: the excess-return leg is $1,000,000 × (5% − 4%) × 1.0 = $10,000/yr level for 10 years; the 10-year annuity factor at 4% is 8.110896, so ED fv = 10,000 × 8.110896 = 81,108.96. host_carrying_value + embedded_derivative_fv = withheld balance (the bifurcation reconciles). MODCO001 is the zero-excess control (asset total return equals host funding rate ⇒ embedded derivative = 0), a sign/identity check. Output schema (embedded_derivative_fv, ed_credit_spread_value, ed_credit_spread_dv01, host_carrying_value, …) is declared on the engine_registry.yaml entry outputs and consumed in-process — there is no cross-codebase boundary contract (so contracts: [] is correct, not a gap).

Engine is BUILT and tested; the model remains under_development pending 2L sign-off. The following are genuine, honestly-stated conditionals:

• No firm-calibrated reconciliation (PENDING — not fabricated). The deterministic snapshot runs on documented synthetic treaties. No reconciliation to a disclosed firm embedded-derivative balance (PRU et al.) is asserted — it requires real disclosed inputs (withheld balance, OAS, funding rate, disclosed ED balance) that are not sourced. This element is reported pending in the validation pack (§4), not papered over with synthetic numbers.
• Uncalibrated by design. The engine carries no @uses_assumptions and no A-NNN are registered; economic inputs are treaty inputs via engine_context. Registering firm-calibrated defaults as A-NNN (with the matching decorator and a data-source binding) is a future ratification item — DS-001 is a placeholder; no calibrated data source is bound.
• Regulatory tag APPLIED + tier re-derived (COND-005, RAT-041-v1.0.3) — tier change FLAGGED for 2L. The §8.3 enum extension landed: asc_815 is now a registered regulatory_frameworks value AND a §6.3(b) Tier-1 trigger. The registry is re-tagged to asc_944 + asc_815 + internal, and the materiality tier is re-derived 2 → 1 (Tier-1 trigger (b) asc_815 + trigger (c) audited-financial-statement numbers), reconciling the model-level tier with the engine_registry tier: tier-1 already on insmodel.L4.funds_withheld_modco. The tier re-derivation is a defensible 1L registry act flagged for 2L confirmation (RAT-041-v1.0.4) — it is not self-ratified, and it does not change model state (under_development). (Enum-leg precedent: issue #2002 / PR #2443 for bma_bscr + asc_815.)
• No cross-codebase output contract (by design, not a gap). Engine outputs are declared on the engine entry and consumed in-process (like ReinsuranceEngine); contracts: [] is therefore correct. A contract would only be added if a downstream codebase consumed the output across a boundary.
• Scope. Covers only the funds-withheld / modco total-return embedded derivative. The index-credit embedded derivatives (FIA/RILA/GMxB-on-VA) are out of scope — already covered by insmodel.L4.va_guarantee, insmodel.L4.indexed_annuity, insmodel.L4.rila_model.

Remaining to flip under_development → active (2L work, not 1L): - 2L effective-challenge sign-off (Validation & Audit) per MRM §10.2 / §10.6.

COND-005 status: the asc_815 §8.3 enum extension is landed (governance leg, above 1L); the consequent re-tag + tier 2 → 1 re-derivation are applied by this pass and flagged for 2L confirmation (RAT-041-v1.0.4).

Partial — 1L evidence assembled; 2L sign-off pending. Registry lifecycle: validation_evidence: partial, peer_review.status: pending. The v1.0.0 pack at modelling/validation_evidence/M-041/v1.0.0/ (a thin index mapping MRM §10.5 elements to runnable tests + the snapshot) is on disk. A 2L reviewer running pytest tests/test_funds_withheld_modco_engine.py and model_snapshots.py M-041 in the InsModel checkout reproduces the evidence.

Items 1–3 are 1L deliverables (done). Items 4–5 are honestly conditional: item 4 is data-gated; item 5 is the 2L gate this hand-off requests.

Regulatory / accounting: - ASC 815 (Derivatives and Hedging) — host-vs-embedded-derivative bifurcation; the governing standard for the planned method. - ASC 944 (Financial Services — Insurance / LDTI) — surrounding US-GAAP insurance accounting context for the ceded treaty.

Source data / external: - Prudential Financial (PRU) FY2025 Form 10-K — names funds-withheld / modco embedded-derivative remeasurement as a net-income-volatility driver.

Internal: - firmmodel/engines/funds_withheld_modco_engine.py (FundsWithheldModcoEngine) — the implemented engine. - tests/test_funds_withheld_modco_engine.py — 11 unit tests; Models/scripts/model_snapshots.py M-041 — deterministic snapshot. - modelling/validation_evidence/M-041/v1.0.0/ — the §10.5 evidence index. - Cross-firm 10-K footprint study, "Gap #1" — vertical/research/03_insurance_gap_analysis.md. - Decision 018 (MRM Framework) — Management/decisions/018-mrm-framework-multi-regime.md; the framework under which this card is governed. - ASC 815 enum extension (RAT-041 COND-005) — landed in modelling/charters/mrm_framework.md (§8.3 enum line 608 + §6.3(b) Tier-1 trigger line 407; precedent: issue #2002 / PR #2443 for bma_bscr + asc_815). The consequent M-041 re-tag + tier 2 → 1 re-derivation are applied (this pass) and flagged for 2L confirmation (RAT-041-v1.0.4).

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

• 2026-06-05 — stub created from registry data per Decision 023 Phase 5 / B-07.
• 2026-06-06 — 1L remediation pass (RAT-041 COND-005) — partially reverted, see below. The pass had claimed asc_815 was added to the §8.3 enum and M-041 re-tagged; that enum edit was an over-reach (amending the MRM standard is a governance act, not 1L) and was reverted.
• 2026-06-07 — corrected the COND-005 claim (2L re-review caught a card-vs-artifact contradiction, COND-006). asc_815 is NOT in the §8.3 enum and the registry tag is asc_944 + internal; the enum extension is a tracked governance follow-up (precedent: #2002). Standards Coverage, Limitations, References, and this Change Log reverted from "resolved" to honest "open/pending". No model code, output, or state change. COND-001/002/003/004 remain genuine engine-build / validation prerequisites (honest conditional).
• 2026-06-06 — 2L documentation pass (card text only; no model-state change). Hand-authored Methodology (planned / pending engine build, grounded in the existing ReinsuranceEngine modco-mechanics boundary), Key Assumptions (no A-NNN bound; required families marked to-be-confirmed-at-build), Validation Packet (honest pending state mirroring registry lifecycle), and References. Added missing Standards Coverage, Dependencies, and Output Snapshot sections (matching the gold-standard M-001 structure). Cross-referenced Limitations to the new pending sections and to insightalm #2001. Advanced header marker from to. Output-changing / modeling-code items (engine build, output contract, assumption registration, validation evidence, §8.3 enum) left for ratification — no model state changed.
• 2026-06-28 — 1L build reconciliation (D053, #2308). The engine insmodel.L4.funds_withheld_modco (FundsWithheldModcoEngine) is BUILT, bound, and merged on InsModel main (@engine, 11 tests passing, deterministic snapshot reproducible, SR 11-7 legacy_metadata archived) — but this card and the registry still described the pre-build "planned / pending engine build / validation_evidence: missing" state (a registry-and-card-vs-disk contradiction). Rewrote Methodology (now code-grounded: ASC 815-15 PV-of-excess-leg, OAS decomposition, DV01), Key Assumptions (uncalibrated by design — no @uses_assumptions, no A-NNN; treaty inputs via engine_context — corrects the prior over-claim risk, COND-006), Output Snapshot (real reproducible table: FWH001 ED fv 81,108.96 hand-verifiable, MODCO001 zero-excess control), Components, Validation Packet (partial — §10.5 elements 1–3 done, 4 firm-reconciliation + 5 2L sign-off honestly PENDING), Limitations, References, Standards Coverage. Registry promoted via registry_deltas/M-041.yaml (PROMOTION channel: validation_evidence: partial, change_log: present, honest BUILT notes). Status STAYS under_development — only 2L effective-challenge sign-off flips it to active. contracts: [] and assumptions: [] are correct (in-process outputs; uncalibrated engine), not gaps. asc_815 §8.3 enum re-tag remains a GOVERNANCE follow-up above 1L (COND-005). No model code or output changed; this is the registry/card sync to the already-built engine.
• 2026-06-29 — 1L COND-005 re-tag + tier re-derivation (RAT-041-v1.0.3). With the asc_815 §8.3 enum leg now landed (registered framework + §6.3(b) Tier-1 trigger — verified in mrm_framework.md), applied the consequent 1L registry acts via registry_deltas/M-041.yaml: re-tagged regulatory_frameworks → [asc_944, asc_815, internal] and re-derived materiality.tier 2 → 1 (Tier-1 triggers (b)+(c)), with the §-reasoning recorded in the materiality justification. This reconciles the model-level tier with the engine_registry tier: tier-1 already on the bound engine. The tier change is FLAGGED for 2L confirmation (RAT-041-v1.0.4) — not self-ratified. Updated Standards Coverage, Limitations, References, and the COND-005 status line from "open / governance-follow-up" to "applied / flagged-for-2L". Status STAYS under_development (1L never self-promotes state). No engine code, output, or model state changed.