I. Definition
The Fragility Index measures computational topology within ultra-short maturities (DTE ≤ 2).
Unlike the Numerical Stability Index (NSI), which monitors the 15–45 DTE institutional surface, the Fragility Index isolates the boundary region where time approaches zero. This region exhibits persistent geometric instability due to expiration asymptotics.
The Fragility Index is not a macro signal.
It is a boundary diagnostic.
II. The Geometry of Expiration
As time to expiration $T \to 0$:
- Vega collapses proportionally to $\sqrt{T}$.
- Gamma and curvature terms concentrate.
- The denominator of the Stability Signal ($\text{Vega}^2$) shrinks rapidly.
The stabilizing cushion disappears. Even modest pricing errors produce large curvature interaction. The resulting topology is structurally hostile.
This hostility is not episodic. It is geometric.
III. Current Boundary Reading
The current reading indicates persistent structural compression within the ultra-short lens.
This is typical. The Fragility Index generally operates within a lower stability band relative to the institutional benchmark.
IV. Regime Distribution (0DTE)
| Regime | % Allocation |
|---|---|
| Stable | 61% |
| Oscillatory | 9% |
| Divergent | 4% |
| Singular | 14% |
Singular and Oscillatory regimes remain structurally elevated due to slope collapse and curvature concentration.
V. Interpretation Discipline
An NSI of 52 in the 15–45 DTE lens would indicate severe systemic compression. An NSI of 52 within the 0DTE lens is structurally typical.
The Fragility Index measures expiration geometry, not sentiment.
VI. Structural Context
The Fragility Index serves two purposes:
- Boundary confirmation: ensures that macro NSI readings are not contaminated by asymptotic effects.
- Microstructure awareness: highlights regions where trajectory stress is structurally elevated.
It complements the Structural Compression Tracker.
Note: The Fragility Index is computed under the ≤2 DTE boundary lens and is structurally decoupled from the institutional NSI benchmark.