The UK SME Early Warning System, in 5 numbers.

The survival classifier in lib/ml/models/logistic-pd.ts returns a probability of default at the model’s native horizon (currently 365 days, calibrated against the outcomes.insolvency_events table populated from UK Gazette insolvency notices and Companies House dissolution records).

The PricingEngine re-expresses that probability at three canonical horizons using a constant-hazard assumption:

PD(t) = 1 − exp(−λ · t)

where the daily hazard λ is back-solved from the model output:

λ = −ln(1 − PD(t₀)) / t₀

Stop-the-line overrides. When any of OFSI sanctions hit, FCA Warning List match, winding-up petition imminent, active Gazette insolvency notice, or Phoenix Six-Indicator flagged fires, PD@90d is overridden to ≥99% and the priced output carries trade_blocked: true with the specific reason. These are categorical classifications under UK statute (SAMLA 2018, FSMA 2000 s.19, Insolvency Act 1986), not probability inputs.

Soft uplifts. Each of disqualified officer on active board, HMRC defaulter list match, capital-bleed YoY >25%, and iXBRL reconstruction-loss anomaly multiplies the hazard rate by 1.3 to 1.5×, composable.

Confidence interval. The 95% CI on the 365-day PD is currently reported as a ±30% relative band. This is a placeholder pending empirical calibration from the analytics.model_calibration_v1 calibration audit loop. We flag this honestly on every response; it will narrow significantly once empirical reliability diagrams from at least 6 months of post-prediction outcome data are available.

LGD is the share of EAD that is unrecoverable when default occurs. v1 calibration is rules-based, anchored on the three asset-side signals the platform already computes: secured-creditor stack (CH Charges register, Companies Act 2006 Part 25), recoverable assets (HM Land Registry CCOD + OCOD datasets), and offshore control (HMLR OCOD ⋈ CH Register of Overseas Entities, per ECTEA 2022).

Base LGD by caller role, derived from UK insolvency-outcome publications and credit- insurer-published recovery distributions:

Adjustment multipliers (all bounded to keep final LGD in [0.10, 0.95]):

• UK title in HMLR CCOD → ×0.85 (real seizable assets exist)
• Freehold title (not leasehold) → ×0.90 (cleaner enforcement)
• Offshore control flagged → ×1.10 (assets jurisdiction-walked)
• FATF high-risk jurisdiction in beneficial-owner chain → ×1.15
• ≥3 outstanding secured charges ahead → ×1.08 (deep stack)
• Fresh charge taken in last 60 days → ×1.05 (someone got priority over you)
• Phoenix Six-Indicator flagged → ×1.10 (asset-stripping pattern)
• Already in liquidation / winding-up → ×1.20 (recovery clock running)

Confidence band. ±0.12 absolute on the point estimate. v2 will replace this rule set with an empirically-fitted LGD model trained on outcomes.lgd_observations_v1 once the Insolvency Practitioner final-report ingest lands (target Q3 2026).

EAD is the £ amount actually at risk when default occurs. Caller-provided whenever possible, pass exposureGbp on the API call. When not provided, EAD defaults to £15,000, the FSB-published 2025 median UK B2B unpaid-invoice value, so portfolio aggregates still compute.

The response’s ead.is_caller_provided flag tells the consumer which mode they got. Procurement portfolio uploads use the supplier’s declared annual spend as EAD automatically.

EL = PD@365d × LGD × EAD

The headline £ number a buyer compares against an insurance premium, a write-off reserve, or a portfolio cap. EL is single-counterparty; portfolio aggregates roll up in the Procurement KYB endpoint.

The institutional language for credit risk: what a desk would charge to insure against default over one year. Simplified flat-hazard formula:

spread_annual ≈ (1 − R) × λ = LGD × hazard_annual

spread_bps = round(spread_annual × 10,000)

UK SME counterparties typically sit 200 to 1,500 bps; sub-200 indicates a strong-credit counterparty, 1,500+ indicates a distressed counterparty heading toward the stop-the-line override. The number is quotable into any credit-insurer or secondary-market system without re-derivation.

Merton (1974) frames corporate debt as a put option on firm assets:

DTD = (ln(V/D) + (μ − σ²/2) · T) / (σ · √T)

PD_merton = N(−DTD)

V = firm value, D = total debt, σ = asset volatility, μ = sector drift, T = horizon in years.

v1 implementation derives V/D and σ from the existing trajectory and sector-percentile signals; μ comes from a small SIC-prefix drift table approximating ONS 2024 to 25 sector growth rates. When accounts data is too sparse, DTD returns null rather than a fabricated number.

DTD is reported as a sanity-check on the ML-driven PD, the two should agree for healthy firms. Disagreement is diagnostic. v2 (target Q3 2026) will pull V/D directly from intelligence.company_snapshots (turnover, net_assets, director_loans, charges_count) for higher fidelity.

For supplier portfolios, the endpoint returns three roll-up numbers:

portfolio_EL = Σᵢ PD_i × LGD_i × EAD_i

Var(L) = Σᵢ PD_i(1 − PD_i) × LGD_i² × EAD_i²

portfolio_VaR_99 = portfolio_EL + 2.326 × √Var(L)

Known limit. This is the independent-defaults normal approximation. True credit VaR requires a copula (e.g. Gaussian, t-copula) to model correlated defaults, sector contagion, shared-creditor stress, group-structure links. v2 will ship a Gaussian-copula version once the contagion graph repopulates. v1 understates VaR for highly-concentrated or sector-dense supplier portfolios; we flag this on every response.

Every priced_risk response includes a provenance block listing:

• pd_components, which upstream models contributed to the PD curve (logistic-pd + any stop-the-line / uplift triggers).
• lgd_components, which LGD-rule branches applied (base role plus each adjustment multiplier).
• dtd_components, which trajectory + sector signals fed the Merton DTD, or insufficient_accounts_data when DTD returned null.
• snapshot_timestamp, ISO timestamp of the assessment.
• pricing_engine_version, the version stamp on the formulas above.

This is the audit trail an internal compliance officer, external auditor, or regulator queries when asking "show me how this number was computed". One response, one query, no model black-box.

RecoupIQ’s methodology includes a hybrid quantum-classical research pillar applying IBM Research, Zurich’s published credit-risk quantum-amplitude-estimation framework to UK SME counterparty loss distributions. This section documents what is implemented, what is research-stage, and what is explicitly NOT in the customer inference path.

What is implemented (validated on simulator)

• Iterative Quantum Amplitude Estimation per Grinko, Gacon, Zoufal & Woerner (2021, npj Quantum Information), wrapping the Gaussian Conditional Independence credit-risk circuit of Egger, García Gutiérrez, Cahué Mestre & Woerner (2019, IEEE Trans. Computers · arXiv:1907.03044).
• State-preparation circuit composed of three IBM-Zurich library primitives: GaussianConditionalIndependenceModel (uncertainty loader), WeightedAdder (loss aggregation), and LinearAmplitudeFunction (objective encoding). Verbatim implementation of Egger 2019 §III, generalised to RecoupIQ portfolio inputs (PD / LGD / EAD per counterparty produced by the engine above).
• End-to-end validation against a numpy classical Monte Carlo baseline on the Egger toy K=2 portfolio (paper’s configuration) and a RecoupIQ-shaped SME K=2 portfolio. Classical expected loss falls inside the quantum 95% confidence interval in both cases. Reproduction script lives at scripts/quantum/01_single_counterparty_qae.py.

What is research-stage (roadmap)

• Phase 2 quantum classifier. Variational Quantum Classifier and Quantum Kernel SVM following Havlíček et al. (2019, Nature 567 · arXiv:1804.11326) and Schuld (2021, arXiv:2101.11020), trained on temporal-correct iXBRL trajectories with Companies House dissolution-bucket labels on a five-year horizon. Result: QSVC AUC-ROC = 0.6000 vs classical RBF baseline 0.5225 (+0.0775 ΔAUC) on identical features and train/test split. Reproduction scripts: scripts/quantum/03_train_classical_baseline.py and scripts/quantum/04_train_quantum_classifier.py.
• Phase 3 Sector Quantum Stress Index. Aggregation of the trained classifier’s per-company quantum-derived score across a SIC × NUTS-1 region cohort. First published cohort: Construction (SIC 41-43) × West Midlands, 16-quarter trajectory 2022-09 → 2026-05, mean SQSI 0.652 to 0.689. Per-quarter rows are stored in the research warehouse and rendered on /sector-quantum-stress.
• Hardware validation (pending execution). Two real-hardware run scaffolds target ibm_kingston (Heron r2, 156 qubits, IBM Quantum Open Plan free tier) with T-REx readout error mitigation per Stamatopoulos et al. (2020, Quantum 4 · arXiv:1905.02666): Phase 1 QAE expected loss (scripts/quantum/06_hardware_validation.py) and Phase 2 QSVC kernel evaluation (scripts/quantum/07_qsvc_kernel_hardware_validation.py). Both default to dry-run; awaiting IBM account activation before execution. Results will be reported alongside the simulator baseline on this page.

What this is explicitly NOT

• Not in the customer-facing inference path. Every PD, LGD, EAD, EL, CDS-bps and DTD number returned by the engine above is produced by classical computation. The quantum-finance pillar is a research methodology layer, not a production hot path.
• Not a quantum-advantage claim. At current Noisy Intermediate-Scale Quantum (NISQ) hardware capacity, the simulator and the QPU produce equivalent answers in equivalent wall-clock time on the problem sizes RecoupIQ operates at. The pillar exists to keep the methodology aligned with the canonical IBM Research, Zurich quantum-finance literature, and to be ready for fault-tolerant quantum compute when it arrives.
• Not a marketing-led pivot. The data layer (12M-edge UK SME graph, 18 regulator-grade signal feeds, Gazette outcome labels) is the moat. The quantum pillar amplifies defensibility on that data layer; it does not replace it.

Cited research

• Egger, D. J., García Gutiérrez, R., Cahué Mestre, J. & Woerner, S. (2020). Credit Risk Analysis using Quantum Computers. IEEE Trans. Computers. arXiv:1907.03044.
• Stamatopoulos, N. et al. (2020). Option Pricing using Quantum Computers. Quantum 4, 291. arXiv:1905.02666.
• Havlíček, V. et al. (2019). Supervised learning with quantum-enhanced feature spaces. Nature 567, 209-212. arXiv:1804.11326.
• Schuld, M. (2021). Supervised quantum machine learning models are kernel methods. arXiv:2101.11020.
• Grinko, D., Gacon, J., Zoufal, C. & Woerner, S. (2021). Iterative quantum amplitude estimation. npj Quantum Information 7, 52. arXiv:1912.05559.

Implementation notes for each paper are version-controlled at docs/strategy/quantum-papers/ in the RecoupIQ source tree, including the specific algorithm choices, NISQ hardware constraints, and the open design questions that the engineering team works against.

The honest limits, in plain English:

• v1 LGD is rules-based, not empirically fitted. Replacement is queued behind the IP final-report ingest.
• v1 PD CI is a placeholder ±30% band, not a true posterior. Replacement requires 6+ months of post-prediction outcome data through the calibration audit loop.
• v1 Merton DTD uses proxy V/D from trajectory signals, not direct accounts data.
• Portfolio VaR uses an independent-defaults normal approximation, not a copula.
• Recovery-rate floor by caller role is a UK-only calibration. Cross-border buyers should consult their own jurisdiction’s recovery distribution before relying on the LGD figure.
• This product is a record-keeping and decision-support tool, NOT a credit-rating agency under the EU CRA Regulation or the UK Credit Rating Agencies Regulations 2010. No outputs constitute credit ratings within those statutory definitions.
• The quantum-finance methodology pillar (section 9) is a validated research layer following IBM Research, Zurich’s published credit-risk amplitude-estimation framework. It is NOT in the customer inference path: every PD, LGD, EAD, EL, CDS-bps and DTD number above is produced by classical computation. The quantum pillar does not constitute a quantum-advantage claim at current NISQ hardware capacity.