L1 ⚛ L1-443 ⊙ Testnet

Merton Credit Risk Structural Model

Computational Finance · Credit risk

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⬇ L1-443.md

# ⚛ L1 Principle — Merton Credit Risk Structural Model **ID:** `L1-443` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Finance — *Credit risk* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** firm value vol vector > **📡 Carrier:** N/A · **🌫 Noise:** market gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555259 --- ## 🧠 1. Introduction **Merton Credit Risk Structural Model** is a **nonlinear inverse problem** whose unknown lives in **firm value vol vector** space, within the **Credit risk** sub-domain of **Computational Finance**. Measurements consist of N/A via a **equity option credit inversion** sensing mechanism. The forward operator applies, in order: applies a smooth nonlinear function element-wise; O · newton · system 2eq operator; S · bs · equity as call operator. Observations are corrupted by market gaussian. Existence of the recovered firm_value_vol_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 80); debt_complexity_multiple_tranches dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Market gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Pointwise nonlinearity → O · newton · system 2eq → S · bs · equity as call → **y** (detector). ``` y = `S.bs.equity_as_call` `O.newton.system_2eq` f(·) x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `O.newton.system_2eq` | O · newton · system 2eq operator | | `S.bs.equity_as_call` | S · bs · equity as call operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Finance | | Sub domain | Credit risk | | Carrier | N/A | | Problem class | nonlinear_inverse | | Solution space | firm_value_vol_vector | | Noise model | market_gaussian | | Integration axis | capital_structure | | Difficulty delta | 5 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered firm_value_vol_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 80); debt_complexity_multiple_tranches dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Market gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | CDS_spread_prediction_RMSE_bp | | Secondary | PD_calibration_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `equity_option_credit_inversion` **Center point:** | Parameter | Unit | Value | |---|---|---| | T maturity yr | — | 1 | | R rate percent | — | 3 | | Sigma e percent | — | 30 | | Leverage ratio d v | — | 0.5 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | T maturity yr | — | 0.25 – 5.0 | | R rate percent | — | 0.0 – 10.0 | | Sigma e percent | — | 5 – 100 | | Leverage ratio d v | — | 0.1 – 0.9 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 50 CDS_spread_prediction_RMSE_bp | Metric | Range | |---|---| | Cds spread prediction rmse bp | 5 – 500 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **CDS_spread_prediction_RMSE_bp**, with κ = `2000` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x2efbf5051bb03d694a44a5906b3b18354043018770aedc0550d58bc5aec228af` - **Chain tx hash:** `0x20a563530bc0c6f554d0d41d28074f54c77904246206bfe74a1de96a2afb6141` - **Chain block:** `41555259` --- ## File Mapping This bundle consists of: `L1-443.md`, `L1-443.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-443.md` | Source of truth — edit this | Human or LLM | | `L1-443.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-443`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-443-001 Merton Credit Risk Structural Model — Nominal + Mismatch Specs

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📋 JSON metadata

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    "sub_domain": "Credit risk",
    "title": "Merton Credit Risk Structural Model"
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Credit risk",
  "title": "Merton Credit Risk Structural Model"
}

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