# ⚛  L1 Principle — Hull-White Interest Rate Model Calibration

**ID:** `L1-440` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Computational Finance — *Interest rate modeling*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** short rate parameter vector
> **📡 Carrier:** N/A · **🌫 Noise:** market gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555259

---

## 🧠 1. Introduction

**Hull-White Interest Rate Model Calibration** is a **parameter-estimation problem** whose unknown lives in **short rate parameter vector** space, within the **Interest rate modeling** sub-domain of **Computational Finance**.

Measurements consist of N/A via a **yield curve calibration** sensing mechanism.

The forward operator applies, in order: applies a smooth nonlinear function element-wise; S · trinomial · tree operator; O · chi2 · swaption prices operator.

Observations are corrupted by market gaussian. Existence of the recovered short_rate_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 ~= 100); yield_curve_inversion_error_bp 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 → S · trinomial · tree → O · chi2 · swaption prices → **y** (detector).

```
y = `O.chi2.swaption_prices` `S.trinomial.tree` f(·) x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `N.pointwise` | Applies a smooth nonlinear function element-wise |
| `S.trinomial.tree` | S · trinomial · tree operator |
| `O.chi2.swaption_prices` | O · chi2 · swaption prices operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Computational Finance |
| Sub domain | Interest rate modeling |
| Carrier | N/A |
| Problem class | parameter_estimation |
| Solution space | short_rate_parameter_vector |
| Noise model | market_gaussian |
| Integration axis | term_structure |
| Difficulty delta | 5 |
| L dag | 3 |

## 📡 4. Measurement Model

Existence of the recovered short_rate_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 ~= 100); yield_curve_inversion_error_bp dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Market gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | swaption_vol_RMSE_bp |
| Secondary | bond_price_RMSE_bp |

## 📏 5. Operating Range (Ω)

**Center problem class:** `parameter_estimation` · **Forward operator:** `yield_curve_calibration`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N tenors | — | 8 |
| Vol noise bp | — | 5 |
| A mean reversion | — | 0.1 |
| N swaption expiries | — | 6 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N tenors | — | 3 – 30 |
| Vol noise bp | — | 1 – 50 |
| A mean reversion | — | 0.01 – 0.5 |
| N swaption expiries | — | 3 – 20 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 8 swaption_vol_RMSE_bp

| Metric | Range |
|---|---|
| Swaption vol rmse bp | 1 – 100 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **swaption_vol_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:** `0x362d152ac33dce79c36b54767446bcd213b07fb73f206937741e59bc965dd3e7`
- **Chain tx hash:** `0x301adcd6f6de86d30066fefeef9fbaa4c0a9865b4f809a811e3422fdd57fd6ce`
- **Chain block:** `41555259`

---

## File Mapping

This bundle consists of: `L1-440.md`, `L1-440.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-440.md` | Source of truth — edit this | Human or LLM |
| `L1-440.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.
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> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-440`._
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