Interbank Networks: How One Bank's Losses Become Everyone's Problem

A web of IOUs, not a set of isolated vaults

No modern bank operates as a sealed box. Banks routinely lend reserves to one another overnight, hold each other's bonds, and participate in the same derivatives markets — a dense mesh of mutual obligations that exists because it is efficient: a bank with a temporary cash surplus can earn interest by lending it to a bank with a temporary shortfall, rather than each institution holding a costly idle buffer sized for the worst day of the year. In calm conditions this interbank market is one of the more boring, plumbing-like parts of finance. Its downside only becomes visible once one node in the network actually fails.

The clearing problem: who can pay whom?

Suppose Bank A owes money to Bank B, which owes money to Bank C, and so on, in a network where every bank's ability to pay its own obligations partly depends on what it collects from others — some of whom may themselves be struggling. You cannot solve for who pays what one bank at a time, because each answer depends on every other answer simultaneously. Larry Eisenberg and Thomas Noe formalised this clearing problem in 2001: given each bank's contractual obligations, its external (non-interbank) assets, and the legal principle of limited liability — no bank pays more than it has — there is a unique, internally consistent vector of actual payments that clears the whole network at once, and it can be computed algorithmically even for large systems.

for each bank i:
  total resources_i = external assets_i + Σ (payments actually received from j)
  obligations_i     = Σ (contractual debts owed to others)

  actual payment_i  = min( obligations_i , total resources_i )
                       — limited liability: never pay more than you have

  bank i defaults if total resources_i < obligations_i

this system must be solved for ALL banks simultaneously
(Eisenberg & Noe, 2001: a unique consistent solution always exists)

Capital buffers: the shock absorber

A bank's capital buffer — the equity cushion of assets funded by shareholders rather than depositors or lenders — is what absorbs a loss before it has to be passed on to creditors. A well-capitalised bank hit by a shock from a failing counterparty can simply eat the loss out of its own equity and keep paying everyone else in full, stopping the cascade dead. A thinly capitalised bank passes the shock straight through to its own lenders, who then face the same decision. This is precisely why post-2008 regulation, including the Basel III capital requirements, focuses so heavily on minimum capital ratios: they are not just about protecting any one bank's depositors, they are the network's primary defence against contagion.

Network structure matters as much as the shock itself

A counterintuitive finding from the systemic-risk literature, notably work by Franklin Allen and Douglas Gale, is that network topology has a non-monotonic effect on contagion. A sparsely connected network can let a shock travel like a line of falling dominoes, with nothing nearby to absorb it. A densely connected network, by contrast, can spread the same loss thinly across many counterparties, none of whom individually take a large enough hit to default — effectively diversifying the shock away, the same logic behind spreading risk across a portfolio. The genuinely dangerous configurations tend to sit in between, or involve a small number of highly connected hub banks — often the largest, most interconnected institutions, sometimes labelled globally systemically important banks — whose failure disproportionately affects the whole network precisely because so many other banks are exposed to them at once.

What this simulation lets you probe

The model on this page lets you shock a chosen bank's assets directly and watch default risk propagate outward through an interbank lending network built on the clearing logic above, while you adjust each bank's capital buffer to see how much of a shock the system can absorb before a local problem becomes a systemic one — the same trade-off regulators and central banks weigh when they set capital requirements and monitor the interconnectedness of the banking system.

Frequently asked questions

Try it live

Everything above runs in your browser — open Bank Runs & Financial Contagion and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.