L1 ⚛ L1-438 ⊙ Testnet

Black-Scholes Option Pricing Calibration

Computational Finance · Option pricing

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⬇ L1-438.md

# ⚛ L1 Principle — Black-Scholes Option Pricing Calibration **ID:** `L1-438` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Finance — *Option pricing* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** implied vol surface > **📡 Carrier:** N/A · **🌫 Noise:** market bid ask gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555258 --- ## 🧠 1. Introduction **Black-Scholes Option Pricing Calibration** is a **parameter-estimation problem** whose unknown lives in **implied vol surface** space, within the **Option pricing** sub-domain of **Computational Finance**. Measurements consist of N/A via a **option price calibration** sensing mechanism. The forward operator applies, in order: applies a smooth nonlinear function element-wise; O · chi2 · market price operator; S · newton · root finding 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 ~= 10); bid_ask_spread_percent 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** → Pointwise nonlinearity → O · chi2 · market price → S · newton · root finding → **y** (detector). ``` y = `S.newton.root_finding` `O.chi2.market_price` f(·) x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `O.chi2.market_price` | O · chi2 · market price operator | | `S.newton.root_finding` | S · newton · root finding operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Finance | | Sub domain | Option pricing | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | implied_vol_surface | | Noise model | market_bid_ask_gaussian | | Integration axis | parameter_space | | Difficulty delta | 3 | | L dag | 2 | ## 📡 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 ~= 10); bid_ask_spread_percent 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 | implied_vol_RMSE_bp | | Secondary | price_RMSE_percent | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `option_price_calibration` **Center point:** | Parameter | Unit | Value | |---|---|---| | N strikes | — | 10 | | N maturities | — | 5 | | Moneyness range | — | 0.2 | | Bid ask spread bp | — | 50 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N strikes | — | 3 – 50 | | N maturities | — | 1 – 20 | | Moneyness range | — | 0.05 – 0.5 | | Bid ask spread bp | — | 5 – 500 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 50 implied_vol_RMSE_bp | Metric | Range | |---|---| | Implied vol rmse bp | 5 – 300 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **implied_vol_RMSE_bp**, with κ = `200` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x33b2b64f770b9852cd5f8992910cd18cf894b536e1885a11382f9e0c0d01ec5d` - **Chain tx hash:** `0xe1d1c50b015ba930d0a06caf6ece436cc45094a497c90366a489309d03263be3` - **Chain block:** `41555258` --- ## File Mapping This bundle consists of: `L1-438.md`, `L1-438.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-438.md` | Source of truth — edit this | Human or LLM | | `L1-438.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 `L1-438`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-438.md).
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L2-438-001 Black-Scholes Option Pricing Calibration — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555258,
  "chain_hash": "0x33b2b64f770b9852cd5f8992910cd18cf894b536e1885a11382f9e0c0d01ec5d",
  "chain_tx_hash": "0xe1d1c50b015ba930d0a06caf6ece436cc45094a497c90366a489309d03263be3",
  "domain": "Computational Finance",
  "hardness_fn": {
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    "kappa": 200,
    "metric": "implied_vol_RMSE_bp",
    "type": "epsilon_fn"
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    "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 ~= 10); bid_ask_spread_percent dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Market bid ask gaussian sets the irreducible data-fidelity floor.",
    "secondary": "price_RMSE_percent"
  },
  "physics_fingerprint": {
    "L_DAG": 2.0,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Computational Finance",
    "integration_axis": "parameter_space",
    "noise_model": "market_bid_ask_gaussian",
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      "O.chi2.market_price",
      "S.newton.root_finding"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "option_price_calibration",
    "solution_space": "implied_vol_surface",
    "sub_domain": "Option pricing",
    "title": "Black-Scholes Option Pricing Calibration"
  },
  "size_tiers": {
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    ],
    "allowed_omega_dimensions": [
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      "N_maturities",
      "bid_ask_spread_bp",
      "moneyness_range"
    ],
    "allowed_problem_classes": [
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    ],
    "center_spec": {
      "epsilon_fn_center": "50 implied_vol_RMSE_bp",
      "forward_operator": "option_price_calibration",
      "input_format": "measurement_only",
      "omega": {
        "N_maturities": 5,
        "N_strikes": 10,
        "bid_ask_spread_bp": 50,
        "moneyness_range": 0.2
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "implied_vol_RMSE_bp": [
        5,
        300
      ]
    },
    "omega_bounds": {
      "N_maturities": [
        1,
        20
      ],
      "N_strikes": [
        3,
        50
      ],
      "bid_ask_spread_bp": [
        5,
        500
      ],
      "moneyness_range": [
        0.05,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Option pricing",
  "title": "Black-Scholes Option Pricing Calibration"
}

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