Credit Pricing — Hazard-Rate Family

M-133 is the Credit Pricing (hazard-rate) family — the FinView-resident model that values single-name credit default swaps (CDS) and credit-index futures using a reduced-form, intensity-based survival model. It is FinView-resident: the engines, contract definitions, and tests all live in [redacted]; nothing in this card depends on InsModel actuarial machinery or on any 10-K / firm-disclosed data.

The family is implemented by two FinView L1 engines plus two Gold Copy L1 challengers (per model_registry.yaml::M-133):

• finview.L1.cds_pricer — single-name CDS (finlib/derivatives/cds_pricer.py, class CDSPricer).
• finview.L1.credit_index_futures_pricer — IG/HY credit-index futures as a weighted basket of CDS (finlib/derivatives/credit_index_futures_pricer.py, class CreditIndexFuturesPricer).
• goldcopy.L1.cds_pricer and goldcopy.L1.trs_pricer — independent challenger implementations (the "gold copy"), whose frozen outputs are pinned in finlib/gold_test_derivatives.py and used as cross-check baselines.

Reduced-form hazard-rate CDS pricing. A CDS exchanges two legs. The protection (default) leg pays the buyer (1 - R) * notional at the moment of default; the premium leg is the running spread the buyer pays (quarterly here) for as long as the reference entity survives. Under the reduced-form model, default arrives as the first jump of a Poisson process with intensity (hazard rate) lambda. With a flat hazard, the survival probability is Q(t) = exp(-lambda * t) and the instantaneous default probability over (t-dt, t] is Q(t-dt) - Q(t).

The engine (CDSPricer.compute_fair_value) builds a quarterly payment grid t_i out to maturity T, computes discount factors DF(t_i) (flat risk_free_rate, or interpolated from a supplied zero curve via finlib.curve_builder.interpolate_curve), and forms:

• Premium leg PV = spread * dt * sum( DF(t_i) * Q(t_i) ) plus an accrual-on-default term spread * 0.5 * dt * sum( DF(t_i) * (Q(t_{i-1}) - Q(t_i)) ) — the ISDA convention that, on average, default lands mid-coupon so half a period's premium has accrued.
• Protection leg PV = (1 - R) * sum( DF(t_i) * (Q(t_{i-1}) - Q(t_i)) ).
• Risky PV01 (RPV01) = dt * sum( DF * Q ) + 0.5 * dt * sum( DF * dQ ) — the present value of 1 unit of running spread on the surviving notional, the credit analogue of a swap's annuity.
• Par (breakeven) spread = protection_leg_PV / (notional * RPV01), the spread that sets fair value to zero.
• Fair value / MTM for a protection buyer = protection_leg_PV - premium_leg_PV (sign-flipped for a protection seller).

Hazard bootstrapping from spreads. The hazard itself is not a free parameter — it is bootstrapped from observed credit spreads in finlib/credit_data.py. The closed-form credit-triangle relation lambda = spread / (1 - R) is implemented by get_hazard_rate(rating, recovery, live_spreads=...), and get_survival_probability exponentiates it. For a full term structure, get_piecewise_hazard_curve bootstraps piecewise-constant hazards from the 5-tenor OAS curve (cum_hazard = spread * t / (1 - R), differenced across tenors) — so the family supports both the single-flat-hazard fast path (used by the snapshot) and a bootstrapped term structure. Spreads enter as a live 7-tier FRED ICE-BofA OAS curve (AAA, AA, A, BBB, BB, B, CCC), with 14 S&P notches mapped onto the 7 tiers by linear notch interpolation (_interpolate_notch / _NOTCH_INTERP) and a static maturity multiplier table (_MATURITY_OAS_MULTIPLIER) scaling the base ~5Y spread.

Credit-index futures reuse CDSPricer: CreditIndexFuturesPricer.index_spread prices each rating bucket of the IG (AAA/AA/A/BBB) or HY (BB/B/CCC) composition, takes the weighted-average par spread as the model index spread, and converts spread basis (model_spread - traded_spread) into P&L via the basket RPV01 and a 100 - spread/100 futures-price convention.

Prose. The single most load-bearing assumption is the recovery rate (A-030): because hazard is derived as spread/(1-R), a change in R rescales both the implied hazard and the protection leg's (1-R) payoff, so recovery sits on both sides of the valuation. The credit/hazard curve (A-031) is the model's calibration target — the family deliberately reads hazard from market spreads (live FRED OAS), not from Moody's published cumulative default tables (those exist in credit_data.py as MOODY_CUMULATIVE_PD but feed PD/transition utilities, not the CDS pricing path). The discount curve (A-032) is kept independent of credit, which is the correct reduced-form factorization; the snapshot uses a flat 4% purely for determinism. Per model_registry.yaml::M-133 and data_source_registry.yaml::DS-056, the intended live single-name/CDX feed (DTCC TIWPRR + FRED CDX) is registered planned, not yet wired — until that fetcher lands the family calibrates off the BAML/ICE-BofA OAS proxy, and this proxy substitution is surfaced here per the registry's documentation requirement.

The four additional declared assumptions split cleanly by which path they bind. A-090 (credit spread curve AAA–CCC) and A-091 (spread term structure) govern the live-OAS calibration that feeds get_oas_for_rating → get_hazard_rate in credit_data.py — they are the source-and-interpolation pair sitting directly under A-031's credit-triangle mapping. A-100 (netting benefit) and A-101 (counterparty, the counterparty-domain "Collateral posting threshold" entry — not the like-numbered mortality-domain GMxB-longevity A-101) are not exercised by the standalone CDS/index pricing path; they bind only the CVA-support consumption by M-052, where the family's credit spreads inform counterparty exposure under ISDA netting and CSA collateral terms.

Deterministic single-name run of finview.L1.cds_pricer (CDSPricer) — reproducible, requires no live market data. The credit curve is the frozen 7-tier OAS dict the engine's own unit tests pin to (tests/test_cds_pricer.py::SAMPLE_LIVE_SPREADS); convention is python scripts/model_snapshots.py M-133 (the FinView snapshot harness), asserted by tests/test_cds_pricer.py.

Input: 5Y BBB single-name CDS · 100 bps running spread · 40% recovery · $10,000,000 notional · buy-protection · quarterly premium · 4% flat discount.

The result is internally consistent: the par spread recovers the 130 bps BBB market OAS to four significant figures, confirming the breakeven-spread inversion is the exact left-inverse of the leg PVs (the engine's test_par_spread_consistency re-prices at par and asserts |FV| < 100). Fair value equals protection_leg_PV - premium_leg_PV = 556,548.94 - 428,115.62 = 128,433.32: because the contract pays only 100 bps while the entity's fair spread is ~130 bps, the protection buyer is under-paying and holds a positive mark. These numbers also tie out to the Gold Copy challenger baseline in finlib/gold_test_derivatives.py (CME_CDS_IG_5Y: par_spread_bps 129.9997, rpv01 4.3443, hazard_rate 0.0217) — the par spread and hazard match exactly; RPV01 differs only because the gold-copy position is $1M notional with a slightly different payment grid, not a methodology gap.

The snapshot was executed under two venvs and produced byte-identical output: FinView ([redacted]) and InsModel ([redacted]). Cross-repo determinism holds because the pricing path depends only on numpy plus the FinView source on sys.path.

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

1. No live CDS/CDX feed (DS-056 planned, not wired). Per model_registry.yaml::M-133 and data_source_registry.yaml::DS-056, the intended single-name/index feed (DTCC TIWPRR + FRED CDX) is registered planned. The family currently calibrates hazard off the BAML/ICE-BofA OAS proxy, not from traded CDS quotes. The snapshot goes one step further and uses a frozen test OAS dict for determinism. Implied hazards are therefore proxy-derived, and basis between cash-bond OAS and traded CDS spread is unmodeled.

2. Flat single-name hazard in the primary CDS path. CDSPricer.compute_fair_value uses one flat lambda from get_hazard_rate for the whole term. A bootstrapped piecewise-constant term structure exists (get_piecewise_hazard_curve) but is not invoked by the single-name pricer — only the maturity-multiplier table approximates curve shape. For a 5Y CDS this is mild; for long-dated or steep-curve names it understates term-structure effects.

3. Static maturity multipliers (A-035). _MATURITY_OAS_MULTIPLIER is a fixed step table, not recalibrated to the live term structure each day, as credit_data.py's own docstring notes ("maturity multipliers are static"). The 5Y point is the un-scaled base (1.00×), so the canonical snapshot is unaffected; off-tenor pricing inherits the static shape.

4. Constant recovery; no recovery–default correlation. Recovery is a fixed input (A-030, default 0.40) with no stochastic recovery and no wrong-way correlation between recovery and default intensity. Because hazard is spread/(1-R), recovery error propagates into both implied default probability and the protection payoff — the dominant valuation sensitivity.

5. Index pricer is a weighted single-name basket, not a tranche/correlation model. CreditIndexFuturesPricer averages bucket par spreads with a fixed IG/HY composition; it has no default correlation / copula and cannot price index tranches or capture index-vs-intrinsic (skew) basis.

6. No accrued-coupon / standard-coupon (100/500 bps) settlement mechanics. The pricer values the running-spread MTM and reports an upfront-equivalent, but does not implement the full ISDA standard-coupon + accrued + upfront cash-settlement decomposition used for post-2009 standardized CDS.

7. Cross-repo (FinView-resident) governance. This is a Tier-2 model under §6.3 trigger (b) (feeds Tier-1 CECL M-040 and Counterparty M-052). It is FinView-resident but governed from the InsightALM modelling registry; its documentation_pack in model_registry.yaml currently shows model_card: missing, validation_evidence: missing, change_log: missing, and last_validated_on: null — this card closes the model-card gap; validation-evidence and an independent challenger sign-off remain under-built (BV-032 honesty: stated as gaps, not claimed as complete). The cross-repo governance risk itself is the open 2L finding INV-032 (shared with M-040 / M-130–M-137): the FinView-resident finlib pricing engines are reached from InsModel consumers via sys.path with no packaged/versioned interface and no sibling-aware CI drift gate, so a finlib signature change would not fail InsModel loudly. This card cross-references INV-032; it does not claim the packaged interface or drift gate exists — building them is a tracked remediation item (see below).

Tracked for ratification (not applied in this documentation pass). The following are output-changing / modeling-code / governance items left for ratification, noted here for transparency: produce an independent (2L) validation-evidence pack + peer-review sign-off (par-spread inversion, monotonicity, RPV01, symmetry, plus an effective-challenge write-up vs the Gold Copy challenger) and set last_validated_on / peer_review.signed_off_by / ratification_ref; wire the live DS-056 (DTCC TIWPRR + FRED CDX) single-name/CDX feed so hazard calibration moves off the BAML/ICE-BofA OAS proxy (the snapshot currently uses a frozen test OAS dict); implement the INV-032 remediation (packaged/versioned finlib interface + sibling-aware CI drift gate); optionally invoke get_piecewise_hazard_curve in the single-name CDS path instead of the flat get_hazard_rate, and/or recalibrate the static _MATURITY_OAS_MULTIPLIER table to a live term structure (Limitations 2 and 3). No model outputs were changed in this pass.

Test result at capture: 21 passed (pytest tests/test_cds_pricer.py tests/test_credit_index_futures_pricer.py). Independent (2L) validation sign-off and a formal validation-evidence pack are not yet produced — model_registry.yaml::M-133 shows validation_evidence: missing, peer_review.status: pending, last_validated_on: null.

Standards / methodology: - ISDA Standard CDS Model — the standardized hazard-rate / survival-curve CDS pricing and upfront-conversion model (premium leg vs protection leg, half-period accrual-on-default). Implemented in finlib/derivatives/cds_pricer.py. - J. Hull & A. White, Valuing Credit Default Swaps (reduced-form intensity model) — the lambda, Q(t) = exp(-lambda·t) survival formulation. - D. Duffie & K. Singleton, Credit Risk: Pricing, Measurement, and Management — reduced-form / intensity-based default modeling and the spread ≈ lambda·(1-R) credit-triangle relation. - O'Kane & Turnbull, "Valuation of Credit Default Swaps" (Lehman QCR) — RPV01 / risky annuity and accrual-on-default conventions used in the engine.

Engine source (FinView-resident): - finlib/derivatives/cds_pricer.py — CDSPricer, engine finview.L1.cds_pricer. - finlib/derivatives/credit_index_futures_pricer.py — CreditIndexFuturesPricer, engine finview.L1.credit_index_futures_pricer. - finlib/credit_data.py — get_hazard_rate, get_survival_probability, get_piecewise_hazard_curve, notch interpolation, FRED OAS calibration; engine finview.L0.credit_data. - finlib/gold_test_derivatives.py — Gold Copy challenger baselines (goldcopy.L1.cds_pricer, goldcopy.L1.trs_pricer).

Tests: - tests/test_cds_pricer.py — 6 single-name CDS tests (par consistency, monotonicity, RPV01, symmetry, keys, curve path). - tests/test_credit_index_futures_pricer.py — credit-index futures basket tests.

Internal: - insightalm/modelling/model_registry.yaml::M-133 — registry entry, Tier-2 materiality, engine list, lifecycle, DS-056 proxy note. - insightalm/modelling/data_source_registry.yaml::DS-056 — planned DTCC TIWPRR + FRED CDX feed (PL-07 critical gap). - insightalm/modelling/model_cards/M-001.md — model-card depth exemplar.

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-2 hand-authoring of Methodology, Key Assumptions and Their Justification, Output Snapshot, Limitations and Known Gaps (×7), Validation Packet, and References from the FinView cds_pricer.py / credit_index_futures_pricer.py / credit_data.py engines + gold_test_derivatives.py challenger + bound A-NNN entries. Stub marker advanced from to. No model outputs, back-test numbers, or validation results were fabricated.
• 2026-06-06 — documentation-only accuracy pass. Added the missing Standards Coverage section (ASOP 56 / SR 26-2 §6.3 trigger (b) Tier-2 / internal; no statutory/GAAP accounting standard asserted for this pricing family). Extended Key Assumptions to cover the four declared-but-undocumented entries A-090 / A-091 (live FRED-OAS calibration path) and A-100 / A-101 (CVA-support consumption by M-052), with A-101 disambiguated to the counterparty-domain "Collateral posting threshold" entry vs the unrelated mortality-domain GMxB-longevity A-101. Cited open 2L finding INV-032 (cross-repo finlib drift gate) by ID in Limitation 7, matching the M-040 / M-130 / M-131 pattern, and added a "Tracked for ratification" note enumerating the gated items. No model outputs, back-test numbers, or validation results were fabricated or changed.