EconIAC for Central Banks and Regulators
"Current stress tests add up bilateral losses. This framework computes whether those losses are mutually consistent — and whether the system will amplify or absorb them. The 2008 crisis was an \(H^2\) event that no \(H^0\) or \(H^1\) tool could have predicted."
The problem with current stress tests
The Federal Reserve's DFAST, the EBA stress test, and the ECB's SREP all apply a macroeconomic scenario to each institution's portfolio and aggregate the losses. This is an \(H^0\) computation: it evaluates bilateral exposures independently and adds them up.
It misses two things:
Triangular risk (\(H^1\)): how bilateral losses at each institution propagate through shared counterparties, correlated positions, and common funding sources. XVA desks at sophisticated institutions partially capture this; system-level stress tests do not.
Systemic risk (\(H^2\)): whether individual institutions' triangular risk estimates are mutually consistent. When they are not — when the Pentagon identity fails at the system level — losses amplify rather than absorb. This is the mechanism of financial crises. No existing stress test computes \(H^2\).
What EconIAC provides
The cohomological stress test
A three-tier extension of current stress testing practice:
| Tier | Level | What it computes | Current practice |
|---|---|---|---|
| 0 | \(H^0\) | Sum of bilateral losses | ✅ Standard (DFAST, EBA) |
| 1 | \(H^1\) | Propagation through interaction triangles | Partial (XVA, IMM models) |
| 2 | \(H^2\) | Topological stability: self-limiting or self-amplifying? | ❌ Not done anywhere |
The Tier 2 output is qualitatively different from Tiers 0 and 1: it is not a loss estimate but a stability classification. A system with \(H^2 = 0\) under stress will absorb losses; a system with \(H^2 \neq 0\) will amplify them. This is detectable before any individual institution breaches a threshold.
The \(H^2\) early-warning indicator
The \(H^2\) class of the financial system is computable from market prices of liquid correlation instruments — CDX/iTraxx tranches, correlation swaps, variance dispersion trades — that are observable in real time.
A rising \(H^2\) class signals that institutions' triangular risk estimates are becoming mutually inconsistent. In the 2008 case, this signal was available in ABX tranche pricing from late 2006 — six months before individual institution failures.
Data required: trade repository data (EMIR, FSB-LEI, ECB repo statistics) plus prices of liquid correlation instruments. All available to regulators today.
Computation: finite linear algebra on the Čech complex of the financial interaction diagram. Tractable even for large networks.
The SIFI theorem
Current SIFI designation uses size metrics (total assets, cross-jurisdictional activity) defined by the FSB. These are \(H^0\) metrics.
The topological criterion: an institution is systemically important if and only if its removal changes the \(H^2\) class of the system.
- A large institution with zero \(H^2\) contribution can fail safely.
- A small institution that is a critical node in a large \(H^2\) class cannot.
- Size is neither necessary nor sufficient for systemic importance.
This gives regulators a principled, computable alternative to the current size-based framework — one that identifies systemic importance from network topology rather than balance sheet scale.
\(H^2\)-based capital charges
The Basel III/IV correlation trading book capital charge attempts to capture \(H^1\) risk but uses the Gaussian copula — a parametric model that systematically misspecifies correlation structure. An \(H^2\)-based capital charge would:
- Compute the \(H^1\) class of each institution's pricing sheaf from market prices of triangular instruments (model-free).
- Compute each institution's \(H^2\) contribution to the system.
- Set systemic risk capital proportional to \(H^2\) contribution.
Institutions with zero \(H^2\) contribution need no systemic risk capital surcharge.
Relation to existing systemic risk measures
| Measure | Level | What it misses |
|---|---|---|
| DebtRank (Battiston et al. 2012) | \(H^0\) | All triangular and systemic effects |
| CoVaR (Adrian & Brunnermeier 2011) | \(H^1\) | System-level mutual consistency |
| SRISK (Brownlees & Engle 2017) | \(H^1\) | System-level mutual consistency |
| Flood et al. (2017) Betti numbers | Graph topology | Financial content (pricing sheaf) |
| EconIAC \(H^2\) | \(H^2\) | Nothing — full three-tier picture |
EconIAC subsumes all existing measures and adds the \(H^2\) tier that none of them compute.
The 2008 crisis as an \(H^2\) event
Individual \(H^1\) mortgage risks at each institution were locally reasonable. The cross-institution correlation of mortgage exposures was an \(H^2\) class that no regulator computed. When the \(H^2\) class became non-trivial, the Pentagon identity failed and the cascade began.
An \(H^2\) stress test in 2006 would have shown:
- Individual \(H^1\) mortgage risks: within limits ✓
- System \(H^2\) class: non-trivial and growing — cascade structurally guaranteed ✗
Papers
| Paper | Content |
|---|---|
| 397 — Systemic Risk as \(H^2\) | Cohomological stress test; SIFI theorem; XVA; 2008 analysis |
| 396 — The Unhedgeability Theorem | Unhedgeability theorem; five-instance table; Pentagon identity |
| 398 — The Topology of Risk (Primer) | Plain-language introduction; no mathematics required |
| 291 — The Topology of Conservation | Double-entry accounting as discrete gauge theory |
| 332 — CHZ Fire Sales (in preparation) | Differentiable ABM; sheaf \(H^1\) leads cascade by 2–3 periods |
| 333 — European Sovereign Repo Run (in preparation) | Calibrated to ECB data; 2022 LDI crisis as \(H^2\) event |