Financial Contagion — How Bank Failures Cascade

The interbank network: a directed graph of debt

Modern banks are embedded in a web of bilateral obligations — loans, repos, derivatives, shared exposures — that forms a directed, weighted graph: nodes are institutions, an edge from A to B means A holds a claim on B, and the edge weight is the exposure's notional value. Real interbank networks are sparse but concentrated in a core-periphery structure — a small, densely connected core of large banks surrounded by a periphery of less-connected institutions — a pattern that central banks worldwide map and monitor as part of financial stability analysis.

The Eisenberg-Noe clearing model

The foundational framework, due to Eisenberg and Noe (2001), gives each bank i external assets eᵢ, total nominal liabilities p̄ᵢ, and a relative liability matrix showing what fraction of its debt is owed to each other bank. The system settles at a clearing payment vector p*, where each bank pays either its full obligation or whatever it can afford — external assets plus incoming payments — whichever is smaller. This is a fixed-point equation, and Eisenberg and Noe proved a unique largest solution always exists, computable by iterating the payment rule from "everyone pays in full" downward. A bank defaults exactly when its assets plus incoming payments fall short of its obligations, and in default it pays every creditor the same pro-rata fraction of what's owed.

Clearing payment vector (fixed point):
  p_i* = min( p̄_i,  e_i + Σⱼ p_ji* · π_ji )
Default condition:  e_i + Σⱼ Lⱼᵢ·(pⱼ*/p̄ⱼ) < p̄_i

How failures propagate, and which topologies are fragile

Contagion travels two channels. Direct contagion runs through the balance sheet: bank A defaults, fails to repay bank B, and if the shortfall exceeds B's capital buffer, B defaults too, propagating onward in rounds until no new defaults occur. Indirect contagion works through asset prices — distressed banks selling assets fast (fire sales) depress prices, hurting other banks holding the same assets even with zero direct bilateral exposure, a feedback the Brunnermeier-Pedersen model (2009) formalises as a "liquidity spiral." Network topology strongly shapes fragility: complete networks, where every bank lends to every other, spread each shock thin and resist small failures but can still crack under systemic shocks, while ring networks concentrate exposure in single links and cascade easily. Real core-periphery and scale-free networks share a property Albert-Barabási called "robust yet fragile" — resilient to peripheral failures, extremely vulnerable to a core node going down.

Too-big-to-fail, 2008, and modern stress testing

A bank is too-big-to-fail when its collapse would be too damaging to allow, creating the moral hazard of institutions taking more risk knowing they'll be rescued; since 2011 the Financial Stability Board has designated roughly 30 Global Systemically Important Banks (G-SIBs) by size, interconnectedness, substitutability, complexity and cross-jurisdictional reach, each facing a 1–3.5% extra capital surcharge. The 2008 crisis was precisely this kind of network event: securitisation chains (mortgages → MBS → CDOs → CDO-squared) pushed derivative notionals — around $60 trillion in mortgage-related credit default swaps — vastly beyond the underlying $10 trillion mortgage market, and Lehman Brothers' September 2008 collapse, though not the largest firm to fail, was allowed to proceed without support, breaking money-market funds' "buck," freezing repo markets, and spiking the LIBOR-OIS spread from 10 to over 350 basis points within days. Post-crisis, regulators built stress tests (the US CCAR, the EU/EBA exercises) that increasingly incorporate network contagion — the Bank of England's RAMSI model and the ECB's STAMP€ simulate cascading balance-sheet dynamics across dozens to over a hundred banks — backed by Basel III capital buffers (CET1 minimum 4.5%, conservation and countercyclical buffers, G-SIB surcharges, and TLAC requirements of at least 18% of risk-weighted assets for G-SIBs).

Frequently asked questions

Try it live

Everything above runs in your browser — open Financial Contagion Network, shock a bank, and watch Eisenberg-Noe clearing propagate losses through a network of asset-liability links in real time. Nothing is installed, nothing is uploaded.