L1 ⚛ L1-441 ⊙ Testnet

Monte Carlo Option Pricing

Computational Finance · Monte Carlo simulation

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⬇ L1-441.md

# ⚛ L1 Principle — Monte Carlo Option Pricing **ID:** `L1-441` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Finance — *Monte Carlo simulation* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** option price scalar > **📡 Carrier:** N/A · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555259 --- ## 🧠 1. Introduction **Monte Carlo Option Pricing** is a **parameter-estimation problem** whose unknown lives in **option price scalar** space, within the **Monte Carlo simulation** sub-domain of **Computational Finance**. Measurements consist of N/A via a **monte carlo path simulation** sensing mechanism. The forward operator applies, in order: S · mc · path generation operator; O · discounting · expectation operator; adds a prior term that biases the solution toward smoothness/sparsity. Observations are corrupted by additive Gaussian noise. Existence of the recovered option_price_scalar 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); discretization_error_Euler_Milstein dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → S · mc · path generation → O · discounting · expectation → **y** (detector). ``` y = `O.discounting.expectation` `S.mc.path_generation` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.mc.path_generation` | S · mc · path generation operator | | `O.discounting.expectation` | O · discounting · expectation operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.regularize` | Adds a prior term that biases the solution toward smoothness/sparsity | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Finance | | Sub domain | Monte Carlo simulation | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | option_price_scalar | | Noise model | gaussian | | Integration axis | simulation_paths | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered option_price_scalar 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); discretization_error_Euler_Milstein dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | price_standard_error_percent | | Secondary | price_bias_percent | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `monte_carlo_path_simulation` **Center point:** | Parameter | Unit | Value | |---|---|---| | N paths | — | 10000 | | Sigma vol | — | 0.2 | | N timesteps | — | 100 | | T maturity yr | — | 1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N paths | — | 1000 – 10000000.0 | | Sigma vol | — | 0.05 – 0.8 | | N timesteps | — | 10 – 1000 | | T maturity yr | — | 0.1 – 10.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.5 price_standard_error_percent | Metric | Range | |---|---| | Price standard error percent | 0.01 – 5.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **price_standard_error_percent**, with κ = `100` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x5ecc3f0ab38af6c3204ae3d349c809268ffa2bf1527f6761e6b57f9b3198c25a` - **Chain tx hash:** `0xf571c624f15786b36078fbe26f1277ec0bf4e58f63802ff20436469a4a3553c7` - **Chain block:** `41555259` --- ## File Mapping This bundle consists of: `L1-441.md`, `L1-441.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-441.md` | Source of truth — edit this | Human or LLM | | `L1-441.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 `L1-441`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-441.md).
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L2-441-001 Monte Carlo Option Pricing — Nominal + Mismatch Specs

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📋 JSON metadata

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  "domain": "Computational Finance",
  "hardness_fn": {
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  "physics_fingerprint": {
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    "integration_axis": "simulation_paths",
    "noise_model": "gaussian",
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      "O.discounting.expectation",
      "O.regularize"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "monte_carlo_path_simulation",
    "solution_space": "option_price_scalar",
    "sub_domain": "Monte Carlo simulation",
    "title": "Monte Carlo Option Pricing"
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      "input_format": "measurement_only",
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        "T_maturity_yr": 1.0,
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        0.01,
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    "omega_bounds": {
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        10000000.0
      ],
      "N_timesteps": [
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        1000
      ],
      "T_maturity_yr": [
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        10.0
      ],
      "sigma_vol": [
        0.05,
        0.8
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Monte Carlo simulation",
  "title": "Monte Carlo Option Pricing"
}

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