EconIAC for Banks and Financial Institutions
"Your XVA desk computes triangular risk (\(H^1\)). Your wrong-way risk model is trying to compute a systemic risk (\(H^2\)) class with \(H^1\) tools. That is why it keeps breaking in stress scenarios."
The three risks on your book
Every risk on a bank's book falls into exactly one of three cohomological levels. Knowing which level determines which instruments hedge it and which models price it.
| Level | Name | Your book | Hedging instrument |
|---|---|---|---|
| \(H^0\) | Bilateral risk | Delta, DV01, single-name credit | Forwards, swaps, single-name CDS |
| \(H^1\) | Triangular risk | Convexity, basis, correlation, CVA, FVA, MVA | Options, swaptions, correlation swaps |
| \(H^2\) | Systemic risk | Wrong-way risk, systemic wrong-way, capital at SIFI threshold | CCP margining, regulatory capital |
This classification is a mathematical theorem (see Paper 396), not a regulatory convention. A bilateral instrument cannot hedge a triangular risk regardless of how many bilateral instruments you hold.
XVA: where your desk lives in this picture
| Adjustment | Level | Why | Hedgeable at desk? |
|---|---|---|---|
| CVA | \(H^1\) | Triangle: you, counterparty, underlying | ✅ Credit options, CDS |
| DVA | \(H^1\) | Triangle: counterparty, you, funding | ✅ Own-name CDS |
| FVA | \(H^1\) | Triangle: you, funding desk, collateral | ✅ Funding swap |
| MVA | \(H^1\) | Triangle: you, CCP, variation margin | ✅ Margin rate swap |
| KVA | \(H^1\)/\(H^2\) | Capital depends on SIFI class (\(H^2\)) | Partial |
| Wrong-way risk | \(H^2\) | Tetrahedron: you, counterparty, market, funding | ❌ Never |
Wrong-way risk is \(H^2\). It is the mutual inconsistency of your CVA, FVA, and DVA triangular risks. Standard XVA models that sum CVA + DVA + FVA + MVA compute \(H^1\) only. The error — the difference between the summed XVA and the true total — is exactly the \(H^2\) wrong-way risk, and it cannot be reduced by any desk-level model regardless of sophistication.
The \(H^2\) component requires system-level data: correlations between counterparty credit quality and market moves across the whole network. This data lives at your CCP and at regulators. The natural model boundary is:
- XVA desk → compute \(H^1\) (CVA, DVA, FVA, MVA)
- CRO / risk management → estimate \(H^2\) wrong-way risk from system data
- Regulator / CCP → provide system-level \(H^2\) correlation data
New capabilities EconIAC provides
Model-free triangular risk pricing
Standard practice: fit a parametric model (Gaussian copula, SABR, HJM) and calibrate to market prices.
EconIAC approach: compute the \(H^1\) class of the pricing sheaf directly from market prices of liquid triangular instruments (CDX tranches, correlation swaps, basket options). No model. No parametric assumption. The \(H^1\) class is the correlation structure — model-free by construction.
Systematic arbitrage detection
A non-trivial \(H^1\) class on any triangle of instruments is a structural market inconsistency: either an arbitrage opportunity or an unhedged risk. EconIAC scans \(H^1\) over all triangles in an instrument universe simultaneously — a topological arbitrage scanner that requires no parametric model and identifies structural inconsistencies that pair-by-pair analysis misses.
KVA at the SIFI boundary
An institution near the SIFI threshold faces KVA that is sensitive to system-level \(H^2\) changes: whether it is designated a SIFI depends on its \(H^2\) contribution to the system, which changes as other institutions' books change. Monitoring the system's \(H^2\) class is commercially valuable to any large institution near the SIFI boundary.
Differentiable contagion models
EconIAC's fire-sale and repo-run models are end-to-end differentiable: the policy gradient \(\partial\text{loss}/\partial\text{haircut}\) is computable in one backward pass. This enables:
- Optimal collateral haircut calibration targeting \(H^1 = 0\)
- Minimum-cost buffer allocation against cascade scenarios
- Reverse stress testing: find the smallest shock that triggers \(H^2 \neq 0\)
The silo problem
Your interest rate desk, FX desk, credit desk, and commodity desk each run separate models calibrated in isolation. Each model is internally valid.
Cross-desk interactions — a rate shock triggering funding stress triggering credit moves — are \(H^2\) effects. They are invisible to any single-desk model because \(H^2\) is a property of the interactions between desks, not of any individual desk.
EconIAC models the full interaction diagram across desks and computes the \(H^2\) class of your book — the mutual inconsistency of your desks' risk estimates under joint stress.
Papers
| Paper | Content |
|---|---|
| 396 — The Unhedgeability Theorem | Unhedgeability theorem; CVA/FVA/convexity as \(H^1\); five-instance table |
| 397 — Systemic Risk as \(H^2\) | XVA section; wrong-way risk as \(H^2\); SIFI theorem; KVA at boundary |
| 299 — XVA as Curvature | CVA/DVA/FVA/MVA as gauge curvature; Burgard–Kjaer PDE as flatness |
| 296 — Term Structure Bundles | HJM convexity as \(H^1\); the \(\frac{1}{2}\) from Maslov = the \(\frac{1}{2}\) from Itô |
| 398 — The Topology of Risk (Primer) | Plain-language introduction; XVA table; wrong-way risk explained |