FLoVo: Flatland-Loop-Void Risk Framework

H^k Risk Stratification for Financial Networks

FLoVo is a Python framework for measuring three strata of financial risk that existing regulatory frameworks (Basel III, VaR, mean-variance optimisation) cannot simultaneously address.

The Three Strata

Flatland (H⁰): Solvency Risk

Question: Can the institution pay its debts?

Measured by: NAV, funding ratio, CET1 capital ratio
Existing instruments: Basel III capital requirements
Status: Adequately regulated

Loop (H¹): Liquidity/Topology Risk

Question: Can it unwind without cascading?

Measured by: β₁ (number of independent funding loops), ρ = β₁/m (load factor), β*(ρ) (critical threshold)
Critical threshold: ρ* ≈ 0.931
Existing instruments: LCR, NSFR, LDI
Status: Partially addressed — miss network-level loops

Void (H²): Systemic Topology Risk

Question: Can the network resolve itself?

Measured by: β₂ (irresolvable conflict cycle count), ΔΔβ₂(i) (marginal contribution per institution)
Existing instruments: G-SIB buffer (proxy only)
Status: NOT regulated — missing from all frameworks

Historical Void Events

All appeared safe on Flatland and Loop metrics until catastrophic failure:

• LTCM (1998): Spread trade topology irresolvable; Fed consortium required
• Lehman/2008: Repo collateral chain conflicts; bilateral resolution impossible
• UK LDI Crisis (2022): Correlated pension fund gilt margin calls; Bank of England intervention required

Quick Start

from flovo import FLoVoProfile
import networkx as nx

# Create or load an exposure graph (nodes=institutions, edges=exposures)
graph = nx.Graph()
# ... add nodes and edges ...

# Compute FLoVo profile
profile = FLoVoProfile.from_graph(graph, nav=1000.0, liabilities=500.0)

# Access risk metrics
print(profile.flatland())          # Solvency
print(profile.loop())              # Loop risk + regime
print(profile.void())              # Void risk (requires econiac integration)

# Risk summary
print(profile.risk_summary())

Installation

pip install flovo

With Full Features (including Void risk)

pip install flovo[finance]  # econiac.forge integration for β₂ computation

API Reference

FLoVoProfile

Main entry point for risk assessment.

• from_graph(graph, nav, liabilities): Create profile from exposure graph
• flatland: Solvency metrics (H⁰)
• loop: Loop risk metrics (H¹)
• void: Void risk metrics (H²) — requires econiac
• risk_summary(): One-line risk assessment

Loop Metrics

• beta_1(graph): Compute β₁ (independent funding loops)
• load_factor(beta_1, num_edges): Compute ρ = β₁/m
• beta_star(rho): Compute β*(ρ) = (3/8)ln(1/(1-ρ))
• Risk regimes: SAT (<30%), MUSHY (30-70%), UNSAT (70-95%), CRITICAL (>95%)

Void Metrics (Requires econiac.forge)

• beta_2(B2_matrix): Compute β₂ from conflict matrix
• delta_beta_2(institution, B2): Compute ΔΔβ₂(i) — marginal systemic contribution

References

• Paper 426 (Beyond Basel): doi:10.5281/zenodo.20701683

  • Regulatory framework for systemic topology risk

• Paper 429 (The Cohomological Fund Manager): doi:10.5281/zenodo.20702221

  • FLoVo application to asset allocation, ALM, and portfolio management

• Paper 430 (The Topology of Intermediation): doi:10.5281/zenodo.20702223

  • FLoVo application to broker-dealers and prime brokerage

• Paper 431 (CCPs Reconsidered): doi:10.5281/zenodo.20702225

  • FLoVo application to central counterparties and default waterfalls

License

MIT License

Author

Ian R. C. Buckley (ian.r.c.buckley@gmail.com)