L1 ⚛ L1-439 ⊙ Testnet

Heston Stochastic Volatility Calibration

Computational Finance · Stochastic volatility

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⬇ L1-439.md

# ⚛ L1 Principle — Heston Stochastic Volatility Calibration **ID:** `L1-439` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Finance — *Stochastic volatility* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** stochastic vol parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** market bid ask gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555258 --- ## 🧠 1. Introduction **Heston Stochastic Volatility Calibration** is a **nonlinear inverse problem** whose unknown lives in **stochastic vol parameter vector** space, within the **Stochastic volatility** sub-domain of **Computational Finance**. Measurements consist of N/A via a **vol surface calibration heston** sensing mechanism. The forward operator applies, in order: applies a smooth nonlinear function element-wise; F · fourier · carr madan operator; O · chi2 · vol surface operator. Observations are corrupted by market bid ask gaussian. Existence of the recovered stochastic_vol_parameter_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 ~= 500); data_sparsity_OTM_options 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 → F · fourier · carr madan → O · chi2 · vol surface → **y** (detector). ``` y = `O.chi2.vol_surface` `F.fourier.carr_madan` f(·) x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `F.fourier.carr_madan` | F · fourier · carr madan operator | | `O.chi2.vol_surface` | O · chi2 · vol surface operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Finance | | Sub domain | Stochastic volatility | | Carrier | N/A | | Problem class | nonlinear_inverse | | Solution space | stochastic_vol_parameter_vector | | Noise model | market_bid_ask_gaussian | | Integration axis | parameter_space | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered stochastic_vol_parameter_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 ~= 500); data_sparsity_OTM_options 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_RMSE_bp | | Secondary | Heston_price_RMSE_percent | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `vol_surface_calibration_heston` **Center point:** | Parameter | Unit | Value | |---|---|---| | N strikes | — | 15 | | N maturities | — | 8 | | Data noise bp | — | 30 | | Max maturity yr | — | 2 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N strikes | — | 5 – 50 | | N maturities | — | 3 – 30 | | Data noise bp | — | 10 – 200 | | Max maturity yr | — | 0.5 – 5.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 60 vol_surface_RMSE_bp | Metric | Range | |---|---| | Vol surface rmse bp | 10 – 500 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **vol_surface_RMSE_bp**, with κ = `10000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x69f3e2451637b97f6c2a1cdd10bb56024ec7ca0ba74f929baa3c0aec3e689c33` - **Chain tx hash:** `0x8ba9e1e8a4ae53459689d357eff7b7f7578dce5df9ae361c6e2b07c1ccb8444c` - **Chain block:** `41555258` --- ## File Mapping This bundle consists of: `L1-439.md`, `L1-439.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-439.md` | Source of truth — edit this | Human or LLM | | `L1-439.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 `L1-439`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-439.md).
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📋 JSON metadata

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    "title": "Heston Stochastic Volatility Calibration"
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  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Stochastic volatility",
  "title": "Heston Stochastic Volatility Calibration"
}

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