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EconIAC for RegTech and Model Vendors

The bilateral/triangular/systemic risk framework is a new product category: cohomological risk infrastructure that no existing vendor provides.

The gap in the market

Current risk infrastructure is built around \(H^0\) and \(H^1\) computations:

  • Market risk systems (Murex, Calypso, Finastra): compute bilateral sensitivities (\(H^0\)) and some triangular Greeks (\(H^1\), via Monte Carlo)
  • XVA engines (Quaternion, Acadia, OpenGamma): compute CVA/DVA/FVA/MVA as \(H^1\) classes, typically via parametric models (Gaussian copula, SABR)
  • Systemic risk platforms (network analysis, DebtRank, CoVaR): compute \(H^0\) bilateral propagation or \(H^1\) conditional risk; none compute \(H^2\)

\(H^2\) — systemic risk as a topological invariant — is unaddressed by any existing vendor. The computation is straightforward linear algebra on the financial interaction diagram. The data (trade repository, CCP exposure data, correlation instrument prices) is available. The market does not yet have a product that does it.

What the EconIAC platform provides

The computational primitives

EconIAC implements the Origami ISA — five operators (SPLIT, SPLAT, FLIP, FLOP, TWIST) that correspond exactly to Čech cohomology operations on the pricing sheaf:

Opcode Cohomology operation Financial meaning
SPLIT Coboundary \(\delta^0: H^0 \to H^1\) Bilateral price → triangular obstruction
SPLAT Integration \(\int_\text{fibre}: H^1 \to H^0\) Triangular risk → price
TWIST Gauge transformation on \(H^1\) Numeraire change, measure change
FLIP Sheaf dualisation \(H^0 \to (H^0)^\vee\) Time reversal, ket → bra
FLOP Trace \((H^0)^\vee \otimes H^0 \to \mathbf{1}\) Probability rule, discounting

These are basis-independent, model-free operations. They compute the exact \(H^1\) and \(H^2\) classes of any financial interaction diagram given market-observable input data.

The differentiable contagion engine

End-to-end differentiable models for all five Hurd contagion channels:

Channel EconIAC module Policy gradient
Solvency cascade finance.contagion.solvency \(\partial\text{loss}/\partial\text{capital\_ratio}\)
Liquidity withdrawal finance.contagion.liquidity \(\partial\text{loss}/\partial\text{coverage}\)
Fire sales finance.contagion.fire_sales \(\partial\text{loss}/\partial\text{haircut}\)
Bank panic finance.contagion.panic \(\partial\text{loss}/\partial\text{threshold}\)
Rehypothecation finance.contagion.rehyp \(\partial\text{loss}/\partial\text{chain\_length}\)

All five channels share the same sheaf structure; the \(H^1\) early-warning signal is computed identically across all five.

The \(H^2\) stability monitor

A real-time \(H^2\) computation pipeline:

from econiac.finance.cohomology import SystemInteractionDiagram, h2_stability

diagram = SystemInteractionDiagram.from_trade_repository(emir_data)
diagram.add_correlation_instruments(cdx_tranches, correlation_swaps)

result = h2_stability(diagram)
# result.h2_trivial: bool — system stable?
# result.critical_triples: list — which institution triples are inconsistent
# result.gradient: dict — ∂H²/∂exposure for each institution pair

Product opportunities

Cohomological stress testing as a service

Regulators need \(H^2\) computation but do not have the infrastructure. A RegTech vendor offering cohomological stress testing as a managed service — ingesting EMIR trade repository data, computing \(H^1\) and \(H^2\), reporting stability indicators — addresses a clear regulatory gap.

Data pipeline: EMIR → bilateral exposure matrix → \(H^1\) triangles → \(H^2\) stability class → regulatory report.

Model-free XVA wrong-way risk

The \(H^2\) component of XVA (wrong-way risk) currently requires parametric models that systematically misspecify correlation structure. A model-free \(H^2\)-based wrong-way risk calculator — using CCP exposure data and correlation instrument prices — would be a commercially differentiated product for XVA desks at major dealers.

Topological SIFI analytics

The FSB's size-based SIFI designation is widely recognised as incomplete. A topological SIFI analytics product — computing each institution's \(H^2\) contribution to the system and identifying critical network nodes — addresses a long-standing regulatory need without requiring legislative change (the \(H^2\) contribution can be reported as a supplementary indicator alongside existing FSB metrics).

Integration

EconIAC is a Python library with:

  • JAX/PyTorch backends for GPU-accelerated computation
  • pysd import for existing Stella/Vensim models
  • Standard financial data connectors (Bloomberg, Reuters, EMIR APIs)
  • RESTful API for integration with existing risk infrastructure
pip install econiac

Papers

Paper Content
396 — The Unhedgeability Theorem Mathematical foundation; unhedgeability theorem; Origami ISA as Čech cohomology
397 — Systemic Risk as \(H^2\) \(H^2\) stress test; SIFI theorem; implementation path
303 — Pacioli Combinator Library Conservation-enforcing DSL; typed financial computation
316 — EconIAC/MONIAC Platform architecture; differentiable ABM foundation