When banks largely finance the synthetic protection they sell, a hidden tipping point emerges: simulations show contagion remains subdued until a warning window (λ ≈ 0.85–0.95) and then explodes at a critical λ* ≈ 0.95 into extreme cascades; limited empirical signals suggest some real-world bank-originated funding but not enough validation, so supervisors should track λ as a compact early-warning feature.

Main Finding

A single structural parameter, λ — the fraction of SRT (Synthetic Risk Transfer) protection that is financed by the originating bank or its affiliates — governs a nonlinear systemic-risk phase transition in bank→NBFI SRT networks. Simulations on directed bank–NBFI networks show a two-stage transition: cascade size departs from baseline at λonset ≈ 0.85–0.95 and then jumps sharply at a critical value λ ≈ 0.95, where extreme “Dragon King” cascade events originate from the circular leverage loop itself. The critical λ is robust to network density, investor concentration, shock size, and tranche thickness; network density controls cascade magnitude once λ is high (observed cascade sizes 0.18–0.61 in the tested density range).

Key Points

• Definition of the loop: circular leverage is summarized by λ, the share of SRT protection weight financed (directly or via affiliates) by the originating bank. High λ means the capital relief banks book is partly self-funded.
• Network model result: in 1,000 random realizations per λ value, contagion cascades show a two-stage phase transition with a sharp cliff at λ* ≈ 0.95.
• Robustness: the location of λ* is invariant across tested variations (network density, investor concentration, shock size, tranche thickness). Density affects cascade magnitude at high λ.
• Tranche sensitivity: rerun at empirically observed median junior-tranche thickness δ = 0.15 (Osberghaus & Schepens, 2026) leaves λ* unchanged but narrows the warning window between onset and the cliff.
• Empirical signals: ECB AnaCredit transaction-level evidence (post-v1) shows banks are 57–66% more likely to sell SRTs to investors they also finance. If pre-deal debt increases are attributed to the SRT, roughly 26% of SRT funding is bank-originated credit.
• Market scale: FSB estimates ≈ USD 220bn of official bank credit lines to private credit funds (commercial estimates USD 270–500bn). BIS/ESRB discuss the same loop as “circles of risk” and note documented scale is modest but data are scarce.
• Public monitoring: six proxy public metrics were ranked by sensitivity to λ*; as of Q2/Q3 2026 five of six show stress signals. SOFR–OIS remained green (consistent with being a lagging indicator).
• Operational point: λ is a single, informative number that would let supervisors place banks on the model’s phase diagram — but it is not reported publicly and is already known internally to each originating bank.

Data & Methods

• Model: directed network model of bank → NBFI SRT relationships. Banks originate loans and sell protection (SRTs) to funds/non-bank investors; some part of that protection is financed by the originating bank or affiliates (captured by λ).
• Simulation design: for each λ value, run 1,000 random network realizations and simulate shock-induced contagion cascades. Key parameters varied include network density, investor concentration, shock size, and tranche thickness.
• Phase diagnostics: identify λonset (departure from baseline cascade-size) and λ* (sharp jump / Dragon King emergence). Report cascade-size ranges across densities at high λ.
• Empirical evidence: transaction-level ECB AnaCredit data (v2), FSB and BIS reports, and literature (Osberghaus & Schepens, 2026) provide calibration points (e.g., median junior-tranche thickness δ = 0.15) and empirical estimates of bank-funded SRT shares.
• Reproducibility: simulation code is MIT-licensed and publicly available (Zenodo DOI: 10.5281/zenodo.19651937; GitHub: github.com/chokmah-me/srt-circular-leverage). The v2 paper PDF, six figures, and a cockpit CSV are included with the paper deposit.

Implications for AI Economics

• Model parsimony and policy signal: compressing a complex bank–NBFI feedback into a single parameter (λ) is attractive for AI-driven systemic-risk monitors and macro-financial agent-based models — it provides a low-dimensional control variable strongly predictive of nonlinear regime shifts.
• Supervision and feature engineering: λ is a potential supervisory feature/label that regulators should require reporting of (or construct from supervisory data). AI models for early warning or stress-testing can use λ directly to map banks onto the phase diagram and detect proximity to the onset/cliff.
• Detection and estimation: the documented empirical correlation (banks 57–66% more likely to sell to financed investors) suggests machine-learning methods applied to granular transaction, balance-sheet, and credit-line data can estimate λ (or proxies) even where direct reporting is missing. Privacy-preserving or federated-learning approaches could help aggregate this sensitive information across institutions.
• Scenario generation & stress tests: the phase-transition behavior and the narrow warning window near λ* implies AI-based stress testers should incorporate nonlinear tipping behavior and train on tail events (Dragon Kings). Standard linear stress methods and lagging market indicators (e.g., SOFR–OIS) will understate risk near the cliff.
• Model transferability: the directed-network + contagion simulation framework and the λ compression approach are transferable to other AI-economics problems involving endogenous feedback loops (for example, margin financing of AI-algorithmic market-makers, or funding loops between platform owners and AI-enabled funds).
• Policy design & interpretability: because λ is interpretable and actionable, it facilitates explainable-AI outputs for regulators (e.g., “bank X has λ=0.92 → within warning window; escalate reporting”). Requiring λ or the underlying inputs improves data availability and reduces reliance on opaque proxies.
• Research and data priorities: to operationalize AI tools, priority should be placed on (i) collecting transaction-level linkages between originators and investors, (ii) standardizing SRT accounting disclosures, and (iii) sharing synthetic or anonymized datasets for model validation — otherwise AI systems will be hampered by the same data scarcity the BIS/ESRB note.

If you want, I can: - Produce a 1-page slide-ready summary for policymakers. - Extract and list the six proxy public metrics and their current signals (if you provide the paper figures/CSV or allow me to parse the v2 deposit).