L1 ⚛ L1-442 ⊙ Testnet

Implied Volatility Surface Construction

Computational Finance · Volatility modeling

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⬇ L1-442.md

# ⚛ L1 Principle — Implied Volatility Surface Construction **ID:** `L1-442` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Finance — *Volatility modeling* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** implied vol surface > **📡 Carrier:** N/A · **🌫 Noise:** market bid ask gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555259 --- ## 🧠 1. Introduction **Implied Volatility Surface Construction** is a **nonlinear inverse problem** whose unknown lives in **implied vol surface** space, within the **Volatility modeling** sub-domain of **Computational Finance**. Measurements consist of N/A via a **vol surface interpolation** sensing mechanism. The forward operator applies, in order: S · interpolation · cubic spline operator; applies a smooth nonlinear function element-wise; O · svi · calibration operator. Observations are corrupted by market bid ask gaussian. Existence of the recovered implied_vol_surface 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 ~= 30); sparse_data_interpolation_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Market bid ask gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → S · interpolation · cubic spline → Pointwise nonlinearity → O · svi · calibration → **y** (detector). ``` y = `O.svi.calibration` f(·) `S.interpolation.cubic_spline` x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.interpolation.cubic_spline` | S · interpolation · cubic spline operator | | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `O.svi.calibration` | O · svi · calibration operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Finance | | Sub domain | Volatility modeling | | Carrier | N/A | | Problem class | nonlinear_inverse | | Solution space | implied_vol_surface | | Noise model | market_bid_ask_gaussian | | Integration axis | strike_maturity | | Difficulty delta | 3 | | L dag | 3 | ## 📡 4. Measurement Model Existence of the recovered implied_vol_surface 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 ~= 30); sparse_data_interpolation_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Market bid ask gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | vol_surface_interpolation_RMSE_bp | | Secondary | arbitrage_violation_count | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `vol_surface_interpolation` **Center point:** | Parameter | Unit | Value | |---|---|---| | N maturities | — | 8 | | Data noise bp | — | 20 | | Max maturity yr | — | 2 | | N strikes per slice | — | 10 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N maturities | — | 2 – 30 | | Data noise bp | — | 5 – 200 | | Max maturity yr | — | 0.1 – 10.0 | | N strikes per slice | — | 3 – 50 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 20 vol_surface_interpolation_RMSE_bp | Metric | Range | |---|---| | Vol surface interpolation rmse bp | 2 – 200 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **vol_surface_interpolation_RMSE_bp**, with κ = `500` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x125a273084cb4217a85bbc193d8af290fb9f1c6e7074568b39ebd214e019b5b5` - **Chain tx hash:** `0x36ed7fac1e9710674227a00de53162061e895752829dcb863b82372f7352a737` - **Chain block:** `41555259` --- ## File Mapping This bundle consists of: `L1-442.md`, `L1-442.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-442.md` | Source of truth — edit this | Human or LLM | | `L1-442.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 `L1-442`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-442.md).
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L2-442-001 Implied Volatility Surface Construction — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555259,
  "chain_hash": "0x125a273084cb4217a85bbc193d8af290fb9f1c6e7074568b39ebd214e019b5b5",
  "chain_tx_hash": "0x36ed7fac1e9710674227a00de53162061e895752829dcb863b82372f7352a737",
  "domain": "Computational Finance",
  "hardness_fn": {
    "delta": 3,
    "kappa": 500,
    "metric": "vol_surface_interpolation_RMSE_bp",
    "type": "epsilon_fn"
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      "license_hash": null,
      "name": "primary",
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    "metric": "vol_surface_interpolation_RMSE_bp",
    "regime": "Existence of the recovered implied_vol_surface 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 ~= 30); sparse_data_interpolation_error dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Market bid ask gaussian sets the irreducible data-fidelity floor.",
    "secondary": "arbitrage_violation_count"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Computational Finance",
    "integration_axis": "strike_maturity",
    "noise_model": "market_bid_ask_gaussian",
    "primitives": [
      "S.interpolation.cubic_spline",
      "N.pointwise",
      "O.svi.calibration"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "vol_surface_interpolation",
    "solution_space": "implied_vol_surface",
    "sub_domain": "Volatility modeling",
    "title": "Implied Volatility Surface Construction"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "vol_surface_interpolation"
    ],
    "allowed_omega_dimensions": [
      "N_strikes_per_slice",
      "N_maturities",
      "data_noise_bp",
      "max_maturity_yr"
    ],
    "allowed_problem_classes": [
      "nonlinear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "20 vol_surface_interpolation_RMSE_bp",
      "forward_operator": "vol_surface_interpolation",
      "input_format": "measurement_only",
      "omega": {
        "N_maturities": 8,
        "N_strikes_per_slice": 10,
        "data_noise_bp": 20,
        "max_maturity_yr": 2.0
      },
      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
      "vol_surface_interpolation_RMSE_bp": [
        2,
        200
      ]
    },
    "omega_bounds": {
      "N_maturities": [
        2,
        30
      ],
      "N_strikes_per_slice": [
        3,
        50
      ],
      "data_noise_bp": [
        5,
        200
      ],
      "max_maturity_yr": [
        0.1,
        10.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Volatility modeling",
  "title": "Implied Volatility Surface Construction"
}

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