Banking And Finance Closed Loop Systems | Bank Runs, Liquidity Spirals, Fire Sales and Financial Contagion

Bank runs, liquidity spirals, fire sales and financial contagion are not four separate stories. They are connected feedback loops in which funding withdrawals, asset sales, price changes, collateral calls, capital losses, confidence and network exposures can reinforce one another. A bank run begins with a funding decision—depositors or short-term lenders want their money back. The bank answers with cash, reserves, liquid assets, secured borrowing, asset sales or emergency funding. Those responses can stabilise the system, or they can create second-round losses that worsen the reason people wanted to leave in the first place.

This guide is built around the search questions readers actually ask: what causes a bank run, can a solvent bank fail from a run, how do fire sales work, what is liquidity contagion, how does systemic risk spread, what is a digital bank run, what role do deposit insurance and central-bank liquidity play, how do bank failures affect other banks, and what is the difference between liquidity and solvency? The answer depends on the starting state. A run can accelerate failure at a weak bank; a funding shock can also damage an otherwise viable institution if it forces destructive sales or blocks settlement. The mechanism is path-dependent, not slogan-dependent.

The current research picture is more nuanced than the old either-or debate. A 2026 New York Fed staff report on bank failures reviews historical evidence and argues that poor fundamentals have usually played a central role in failed-bank episodes, while runs often act as triggers or accelerants rather than the sole root cause. At the same time, current financial-stability research continues to model liquidity spirals, runnable funding, fire sales, margin calls and cross-sector contagion because the feedback channels can amplify shocks across otherwise separate institutions. The useful mathematical question is therefore not “runs or solvency?” but which state variable deteriorates first, which feedback edge amplifies it, and which stabiliser can act before a hard constraint is breached?

Scope. This is an applied-mathematics and systems-thinking article. It is not financial advice, deposit advice, investment advice, prudential compliance advice, crisis-management instruction or a claim that Bukit Timah Tutor is a banking authority. Current institutional rules and protections differ by jurisdiction and should be checked with the competent authority.

50-second router

• For the full lane, start with Banking And Finance Closed Loop Systems | The Complete System.
• For bank survival basics, read Balance Sheets, Liquidity, Capital and the Mathematics of Bank Survival.
• For the core mechanism, read The run–sale–loss–run loop.
• For the research distinction, read Liquidity trigger versus solvency root.
• For digital speed, read When the feedback clock accelerates.
• For market contagion, read Fire sales and common-asset channels.
• For cross-sector contagion, read Banks, funds, margins and market-based finance.
• For worked scenarios, read Contagion laboratory.

The run–sale–loss–run loop

The simplest bank-run loop has five stages. First, funding leaves. Second, the bank uses immediately available liquidity. Third, if outflows exceed that buffer, the bank raises secured or unsecured funding or sells assets. Fourth, funding costs, haircuts or sale discounts can create losses. Fifth, those losses can weaken capital or confidence, producing more outflows. The loop becomes self-reinforcing when the response to the first outflow makes the second outflow more likely.

The opposite is also possible. If the bank has ample cash, diversified funding, credible collateral access and strong capital, the first outflow can be absorbed with limited economic damage. Depositors observe continued payment, stress recedes and the loop becomes stabilising. The same initial withdrawal can therefore lead to recovery in one balance sheet and failure in another.

Mathematically, the key variables are the outflow rate, usable liquid resources, asset-sale elasticity, haircut schedule, funding spread, capital buffer, confidence response and execution delay. A run model without time is incomplete. A bank with enough total assets can still fail if usable liquidity arrives after the deadline.

Liquidity trigger versus solvency root

A bank can fail because it is insolvent: the economic value of its assets is insufficient relative to liabilities. It can also experience an acute liquidity problem: obligations come due faster than usable cash arrives. The two mechanisms interact, which is why postmortems often resist clean classification.

The 2026 New York Fed staff report Bank Failures: The Roles of Solvency and Liquidity reviews historical evidence and argues that failed banks with runs have often also had poor fundamentals. That finding pushes against the oversimplified story that a random panic routinely destroys otherwise strong banks. It does not imply liquidity management is unimportant. A weak bank still fails through a path, and runs can determine the speed, loss realisation and spillover pattern of that path.

The Richmond Fed’s 2026 explainer likewise frames the conceptual distinction clearly: under a pure liquidity view, withdrawals can force a healthy bank into fire-sale losses; under a solvency view, weak assets are the underlying problem and the run exposes or accelerates it. The closed-loop method keeps both channels in the model and asks which dominates in the specific case.

Runnable funding: the liability-side vulnerability

Runnable funding is funding that can leave quickly. Demand deposits, uninsured large deposits, short-term wholesale borrowing, some repo funding and redeemable investment vehicles can all create forms of rapid liquidity demand under different institutional rules. What matters is not the label alone but the behavioural and contractual ability to exit.

The Federal Reserve’s financial-stability framework highlights elevated funding risk when institutions promise short-notice redemption while holding illiquid or long-maturity assets. This maturity and liquidity transformation can create incentives to withdraw quickly under stress. A balance sheet can therefore become fragile even before losses occur if its liabilities are faster than its assets.

A useful vulnerability concept is runnable liabilities relative to immediately usable liquid resources. A 2024 Federal Reserve note on the interaction of bank leverage, interest-rate risk and runnable funding makes this coupling explicit. The insight is that funding structure, asset duration and capital flexibility should be analysed together, not as independent checklists.

When the feedback clock accelerates

Digital banking reduces the time between decision and execution. A depositor can read a message, open an app and initiate a transfer quickly. This does not create a run by itself. It changes the speed at which behavioural feedback can become balance-sheet reality.

Suppose a bank could historically mobilise 10 units of collateral per hour while deposit outflow arrived at 5 per hour. The controller was faster than the disturbance. If digital coordination raises outflow to 25 per hour while collateral mobilisation remains at 10, the same balance sheet can become fragile even though the total potential outflow has not changed. Speed changes solvency-through-liquidity pathways because it can force earlier asset sales.

The relevant variables are withdrawal velocity, communication velocity, operational settlement capacity, collateral mobilisation time, market execution time and central-bank facility access time. More liquid assets are not enough if they cannot be converted in the required interval.

Fire sales: when private liquidity defence changes market prices

A fire sale occurs when an institution sells assets quickly under pressure, often into a market unable to absorb the volume without a price discount. The sale improves the seller’s cash position but can reduce asset values for every institution holding the same security. One bank’s defensive action can therefore damage another bank’s capital.

The Federal Reserve’s financial-stability material identifies this channel directly: a run can force asset sales at distressed prices, creating losses and potentially insolvency. The Reserve Bank of Australia’s stress-testing work likewise models how fire sales can push down prices and affect the capital ratios of other banks holding the same assets. This is the common-asset contagion channel.

A simple price-impact model can write sale discount as a function of quantity relative to market depth. If one bank sells 1% of normal daily volume, price impact may be small; if many banks simultaneously sell ten times normal volume, impact can become nonlinear. The exact function is market-specific, but the systems lesson is general: liquidity is endogenous to collective behaviour.

Common holdings create contagion without direct lending links

Two banks do not need to lend to each other for stress to propagate. If both hold the same securities and one is forced to sell, the resulting price decline can mark down the other bank’s portfolio. The second bank may then breach a risk limit, face collateral calls or decide to sell too. This creates indirect network contagion through asset similarity.

The network can be represented as a bipartite graph: banks on one side, assets on the other. Edge weights represent holdings. An asset with many large holders creates overlap. A bank with many concentrated positions creates sensitivity. When prices move endogenously with sales, the graph becomes a dynamic feedback network rather than a static exposure matrix.

The specialist BTT route How Interbank Networks Transmit Bank Stress owns the detailed graph mechanism. This article places that network inside the larger run-and-liquidity loop.

Direct counterparty contagion

Direct contagion occurs when one institution owes money to another and cannot pay in full. The creditor takes a loss, reducing its own capital. If the creditor was thinly capitalised or highly exposed, it can fail too. Bilateral exposure matrices and clearing models make this pathway explicit.

The direction and severity depend on netting, collateral, seniority, recovery, maturity and legal structure. A gross exposure of 100 may produce a much smaller net loss after collateral or set-off, or a much larger liquidity problem if settlement timing creates a temporary gross need. Exposure amount alone is therefore an incomplete contagion measure.

Closed-loop modelling asks whether the creditor changes behaviour after the loss: reduces lending, hoards liquidity, sells assets or pulls funding from others. The second-round response can create a larger system effect than the original direct loss.

Funding contagion through information

Stress can spread because creditors and depositors use one institution’s failure as information about another. If banks share similar business models, asset exposures, depositor profiles or accounting risks, a failure can trigger Bayesian updating across the sector. Funding spreads widen even at institutions with no direct exposure to the failed bank.

This is not necessarily irrational panic. Sometimes one failure reveals a common vulnerability. Sometimes investors overgeneralise. Systems analysis should not assume which. The measurable question is how much of the funding response can be explained by shared fundamentals versus pure network spillover.

Information contagion is especially important when balance sheets are opaque. Uncertainty can create a lemons problem in which strong and weak institutions are temporarily priced together. Transparency can reduce uncertainty, but disclosure also has to be timely, credible and interpretable.

Margin spirals connect markets to funding

Leveraged investors and banks may have to post additional collateral when prices move against them. A margin call creates immediate cash demand. To raise cash, institutions sell assets. Those sales can push prices further in the same direction, causing more margin calls. The result is a margin spiral.

The IMF’s 2026 work on systemwide stress testing emphasises this cross-sector channel, especially among non-bank financial intermediaries and market-based finance. Central clearing reduces some bilateral counterparty risk but can concentrate liquidity demands through variation margin and default-resource requirements. Risk is transformed, not erased.

A closed-loop margin model therefore needs both solvency and liquidity variables. The hedge can reduce mark-to-market exposure while the margin process creates a same-day funding need. An institution can be economically hedged and operationally short of cash.

Banks, funds and non-bank financial intermediaries

Modern contagion does not stop at bank balance sheets. Investment funds can face redemptions, insurers can face collateral calls, hedge funds can face margin and prime-broker constraints, and money-market funds can face liquidity pressure. Banks connect to these entities through credit lines, repo, derivatives, custody, payment services and common asset markets.

The IMF’s August 2026 systemwide stress-testing paper specifically integrates non-bank financial intermediary risks because shocks can spread across sectors through runs, redemptions, margin calls, fire sales and market-price dynamics. The relevant network is therefore broader than the interbank market.

The systems challenge is feedback across different regulatory and accounting regimes. A fund may sell because of redemptions; a bank may sell because of liquidity or capital; a dealer may reduce inventory because of risk limits. The market sees all sales as supply. Different causes can combine into one price shock.

Deposit insurance changes the depositor decision rule

Deposit insurance can reduce the incentive for covered depositors to run because eligible deposits are protected up to the applicable terms and limits. The exact coverage, funding and payout arrangements differ by jurisdiction, so no generic global number belongs in a world-facing article.

From a control perspective, deposit insurance changes the payoff matrix. If an eligible depositor believes repayment is credible even if the bank fails, the private benefit of racing other depositors to withdraw is reduced. This can dampen coordination-driven runs.

Insurance does not make asset losses disappear. It changes who bears them and how failure is managed. It also creates incentive-design questions, which is why insurance is paired with supervision, capital, resolution and other controls rather than treated as a complete substitute for prudence.

Central-bank liquidity as a time-buying mechanism

Central banks can provide liquidity to eligible institutions under defined rules and against eligible collateral. The systems purpose is to turn collateral into settlement-ready funding when private markets are impaired or too slow. This can stop a liquidity spiral before forced sales destroy value.

Liquidity support does not repair insolvency. If assets are fundamentally worth less than liabilities, borrowing against those assets can buy time but not create missing economic value. This is why central-bank lending frameworks distinguish liquidity provision from resolution and why collateral, pricing and eligibility matter.

Operational readiness is part of the control loop. A bank that theoretically owns eligible collateral but has not pre-positioned, documented or tested access may discover that emergency liquidity arrives too late. The controller must be executable, not merely available in policy.

Recovery and resolution are different states

Recovery is the institution’s attempt to restore viability while still operating. Actions can include raising capital, reducing distributions, selling businesses, shrinking exposures or strengthening liquidity. Resolution begins when authorities use special tools to manage failure and preserve critical functions under the applicable legal framework.

The Federal Reserve describes recovery and resolution planning as preparation for severe stress and, if failure occurs, rapid and orderly resolution. Different jurisdictions implement different tools, but the system purpose is shared: avoid an uncontrolled collapse of payment, deposit and credit functions.

In state-machine terms, recovery attempts to push the bank from stress back to normal. Resolution moves the institution into a different rule regime. The mistake is to continue applying normal-state optimisation once viability is lost.

Alicia, Tricia and Kai Kai read a run differently

Alicia watches the timeline. At 9:00 deposits fall 5. At 10:00 they fall another 10. At 10:30 a news event accelerates outflows to 25 per hour. At 11:00 collateral can be mobilised only at 8 per hour. Her diagnosis is a speed mismatch. The amount of assets may be adequate in theory, but the response is slower than the disturbance.

Tricia watches valuation. The bank sells securities with carrying value 100 for 92. The 8 loss reduces equity. The next 100 sale occurs in a thinner market and clears at 88. Her diagnosis is endogenous loss: liquidity defence is eroding solvency.

Kai Kai watches the network. Other banks hold the same securities, funds face redemptions and secured lenders increase haircuts. His diagnosis is contagion: one institution’s response has become a system input. The right question is no longer whether the first bank survives but whether market functioning survives.

Contagion laboratory: 36 worked mini-cases

1. Runoff velocity

Setup. Deposits 1,000; 200 leaves in ten hours.

Closed-loop reading. Average runoff is 20 per hour, but the peak hourly rate matters more if liquidity mobilisation is nonlinear. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

2. Acceleration

Setup. The same 200 outflow occurs in two hours.

Closed-loop reading. Total loss is unchanged but average velocity rises to 100 per hour, compressing response time by five times. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

3. Liquidity coverage

Setup. Usable buffer 250; stressed outflow 180.

Closed-loop reading. A simple excess of 70 remains before second-round calls and haircuts. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

4. Buffer failure

Setup. Usable buffer 250; outflow jumps to 320.

Closed-loop reading. A 70 funding gap appears before other sources. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

5. Fire-sale loss

Setup. Assets carrying 100 sell for 94.

Closed-loop reading. Liquidity rises 94 while a 6 economic loss is crystallised. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

6. Second sale

Setup. Another 100 block sells for 88 after market depth falls.

Closed-loop reading. Marginal price impact worsens, showing nonlinear sale cost. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

7. Common holdings

Setup. Another bank owns 500 of the same asset and marks it down 6%.

Closed-loop reading. A 30 mark-to-market decline can hit the second bank without direct counterparty exposure. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

8. Haircut shock

Setup. Collateral 200 moves from 10% to 25% haircut.

Closed-loop reading. Lendable value falls from 180 to 150. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

9. Margin call

Setup. Same-day collateral requirement rises 40.

Closed-loop reading. Liquidity need increases 40 even if long-term expected P&L is unchanged. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

10. Wholesale rollover

Setup. 100 funding matures and only 60 rolls.

Closed-loop reading. A 40 replacement need appears. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

11. Spread shock

Setup. Rolled funding reprices 300 basis points higher on 200.

Closed-loop reading. Annualised funding expense rises about 6 before hedging or tax. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

12. Capital erosion

Setup. Equity 80; fire-sale loss 20.

Closed-loop reading. One quarter of starting equity is consumed. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

13. Leverage amplification

Setup. Assets 1,000, equity 50; asset values fall 3%.

Closed-loop reading. A 30 loss consumes 60% of equity. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

14. Deposit concentration

Setup. One depositor holds 150 of 1,000.

Closed-loop reading. A single exit removes 15% of deposits. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

15. Top-five concentration

Setup. Five depositors hold 400 of 1,000.

Closed-loop reading. Correlated behaviour can overwhelm average retail runoff assumptions. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

16. Payment queue

Setup. Outflows settle faster than incoming receipts by 30 per hour.

Closed-loop reading. Queue or reserve need grows 30 per hour absent new liquidity. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

17. Collateral delay

Setup. Eligible collateral exists but requires three hours to mobilise while funding is due in one hour.

Closed-loop reading. Theoretical capacity does not solve the deadline. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

18. FX liquidity

Setup. Aggregate liquidity surplus 50 but the bank has a USD deficit 30.

Closed-loop reading. The relevant currency can be short despite group surplus. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

19. Entity trap

Setup. Group buffer 500 but only 40 can be transferred to the stressed subsidiary today.

Closed-loop reading. Usable local liquidity is 40. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

20. Information spillover

Setup. A peer failure raises the bank’s wholesale spread despite no direct exposure.

Closed-loop reading. Funding contagion arrives through beliefs rather than balance-sheet claims. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

21. Counterparty loss

Setup. Bank A loses 20 on default of Bank B.

Closed-loop reading. A’s capital falls 20 and may trigger its own defensive actions. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

22. Netting benefit

Setup. Gross bilateral obligations 100 each direction.

Closed-loop reading. Net exposure can be far smaller if enforceable netting applies, reducing direct loss and liquidity needs. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

23. Wrong-way collateral

Setup. Counterparty defaults when pledged collateral also falls 25%.

Closed-loop reading. Recovery protection weakens precisely when needed. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

24. Fund redemption

Setup. A fund faces 15% redemption and sells common bank-held assets.

Closed-loop reading. Non-bank redemption can transmit market loss back to banks. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

25. CCP margin

Setup. Volatility doubles and margin calls rise sharply.

Closed-loop reading. Central clearing can reduce bilateral credit risk while increasing liquidity demand. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

26. Central-bank funding

Setup. Bank pledges 100 collateral at a 20% haircut.

Closed-loop reading. It can raise about 80 under the simplified assumption, buying time but adding a liability. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

27. Deposit insurance

Setup. Covered depositors have credible protection.

Closed-loop reading. The incentive to race for withdrawal can fall, changing the behavioural runoff model. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

28. Communication effect

Setup. Transparent disclosure reduces uncertainty about asset losses.

Closed-loop reading. Information feedback can stabilise funding if credible; vague reassurance may not. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

29. Capital raise

Setup. New equity 50 arrives after losses.

Closed-loop reading. Equity and liquidity can improve if cash is injected, but execution delay matters. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

30. Asset shrinkage

Setup. Bank lets 100 loans run off and uses cash to reduce volatile funding.

Closed-loop reading. Balance-sheet scale and refinancing need fall together. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

31. Credit contraction

Setup. Multiple banks reduce lending after losses.

Closed-loop reading. Private resilience actions can reduce system credit supply and affect the economy. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

32. Price feedback

Setup. Asset sales lower prices, which worsen margin at other institutions.

Closed-loop reading. Market prices become an endogenous transmission channel. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

33. Run threshold

Setup. Outflow behaviour jumps once a public ratio crosses a perceived threshold.

Closed-loop reading. The system exhibits regime change rather than smooth linear runoff. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

34. Operational outage

Setup. Depositors cannot see updated balances during stress.

Closed-loop reading. Operational uncertainty can amplify confidence shocks even if liquidity is adequate. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

35. Social coordination

Setup. Many depositors receive the same warning simultaneously.

Closed-loop reading. Correlation in decision timing raises peak outflow without changing total deposit base. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

36. Recovery boundary

Setup. Contingency actions restore liquidity before capital is materially impaired.

Closed-loop reading. The loop can be stabilised before entering resolution. Then ask which second-round variable changes: confidence, haircut, funding spread, market price, capital, queue length or credit supply.

Systemic-risk matrix: 200 propagation tests

Propagation 1: how rapid withdrawal travels through retail deposits

Start with the role of retail deposits: customer funding that can leave. Shock the node by rapid withdrawal, which can compress the funding clock. Measure withdrawal velocity and concentration, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through cash, reserves or asset monetisation. If instead outflows exceed same-day replacement, the node becomes a transmitter. Remember that time is the first constraint. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 2: feedback test for retail deposits

Treat retail deposits as a network component rather than an isolated balance-sheet line. Its system function is customer funding that can leave. Under loss revelation, change beliefs about asset value. Track withdrawal velocity and concentration and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether cash, reserves or asset monetisation; contagion appears when outflows exceed same-day replacement. Because information becomes funding risk, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 3: second-round effects from retail deposits

retail deposits provide customer funding that can leave. After market-price gap, reduce collateral and capital values. Measure withdrawal velocity and concentration before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires cash, reserves or asset monetisation. When outflows exceed same-day replacement, the shock becomes contagious. The core insight is that valuation becomes liquidity. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 4: retail deposits under haircut increase

retail deposits are modelled here as customer funding that can leave. Apply haircut increase: lower secured funding capacity. Observe withdrawal velocity and concentration. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is cash, reserves or asset monetisation. The failure condition is that outflows exceed same-day replacement. The systems lesson is that collateral rules amplify price stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 5: how margin spike travels through retail deposits

Start with the role of retail deposits: customer funding that can leave. Shock the node by margin spike, which can create same-day cash demand. Measure withdrawal velocity and concentration, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through cash, reserves or asset monetisation. If instead outflows exceed same-day replacement, the node becomes a transmitter. Remember that risk transfer becomes liquidity demand. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 6: feedback test for retail deposits

Treat retail deposits as a network component rather than an isolated balance-sheet line. Its system function is customer funding that can leave. Under wholesale closure, remove refinancing channels. Track withdrawal velocity and concentration and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether cash, reserves or asset monetisation; contagion appears when outflows exceed same-day replacement. Because maturity transformation is exposed, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 7: second-round effects from retail deposits

retail deposits provide customer funding that can leave. After payment outage, delay settlement and create uncertainty. Measure withdrawal velocity and concentration before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires cash, reserves or asset monetisation. When outflows exceed same-day replacement, the shock becomes contagious. The core insight is that operations become finance. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 8: retail deposits under counterparty default

retail deposits are modelled here as customer funding that can leave. Apply counterparty default: create direct loss and replacement need. Observe withdrawal velocity and concentration. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is cash, reserves or asset monetisation. The failure condition is that outflows exceed same-day replacement. The systems lesson is that network claims transmit stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 9: how rating downgrade travels through retail deposits

Start with the role of retail deposits: customer funding that can leave. Shock the node by rating downgrade, which can raise spreads and collateral requirements. Measure withdrawal velocity and concentration, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through cash, reserves or asset monetisation. If instead outflows exceed same-day replacement, the node becomes a transmitter. Remember that external classification changes behaviour. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 10: feedback test for retail deposits

Treat retail deposits as a network component rather than an isolated balance-sheet line. Its system function is customer funding that can leave. Under regime change, invalidate normal-period correlations. Track withdrawal velocity and concentration and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether cash, reserves or asset monetisation; contagion appears when outflows exceed same-day replacement. Because historical averages understate nonlinear stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 11: second-round effects from large corporate deposits

large corporate deposits provide concentrated operational or treasury balances. After rapid withdrawal, compress the funding clock. Measure top-account share and correlation before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires relationship retention and liquidity buffer. When one decision creates a cliff, the shock becomes contagious. The core insight is that time is the first constraint. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 12: large corporate deposits under loss revelation

large corporate deposits are modelled here as concentrated operational or treasury balances. Apply loss revelation: change beliefs about asset value. Observe top-account share and correlation. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is relationship retention and liquidity buffer. The failure condition is that one decision creates a cliff. The systems lesson is that information becomes funding risk. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 13: how market-price gap travels through large corporate deposits

Start with the role of large corporate deposits: concentrated operational or treasury balances. Shock the node by market-price gap, which can reduce collateral and capital values. Measure top-account share and correlation, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through relationship retention and liquidity buffer. If instead one decision creates a cliff, the node becomes a transmitter. Remember that valuation becomes liquidity. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 14: feedback test for large corporate deposits

Treat large corporate deposits as a network component rather than an isolated balance-sheet line. Its system function is concentrated operational or treasury balances. Under haircut increase, lower secured funding capacity. Track top-account share and correlation and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether relationship retention and liquidity buffer; contagion appears when one decision creates a cliff. Because collateral rules amplify price stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 15: second-round effects from large corporate deposits

large corporate deposits provide concentrated operational or treasury balances. After margin spike, create same-day cash demand. Measure top-account share and correlation before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires relationship retention and liquidity buffer. When one decision creates a cliff, the shock becomes contagious. The core insight is that risk transfer becomes liquidity demand. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 16: large corporate deposits under wholesale closure

large corporate deposits are modelled here as concentrated operational or treasury balances. Apply wholesale closure: remove refinancing channels. Observe top-account share and correlation. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is relationship retention and liquidity buffer. The failure condition is that one decision creates a cliff. The systems lesson is that maturity transformation is exposed. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 17: how payment outage travels through large corporate deposits

Start with the role of large corporate deposits: concentrated operational or treasury balances. Shock the node by payment outage, which can delay settlement and create uncertainty. Measure top-account share and correlation, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through relationship retention and liquidity buffer. If instead one decision creates a cliff, the node becomes a transmitter. Remember that operations become finance. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 18: feedback test for large corporate deposits

Treat large corporate deposits as a network component rather than an isolated balance-sheet line. Its system function is concentrated operational or treasury balances. Under counterparty default, create direct loss and replacement need. Track top-account share and correlation and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether relationship retention and liquidity buffer; contagion appears when one decision creates a cliff. Because network claims transmit stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 19: second-round effects from large corporate deposits

large corporate deposits provide concentrated operational or treasury balances. After rating downgrade, raise spreads and collateral requirements. Measure top-account share and correlation before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires relationship retention and liquidity buffer. When one decision creates a cliff, the shock becomes contagious. The core insight is that external classification changes behaviour. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 20: large corporate deposits under regime change

large corporate deposits are modelled here as concentrated operational or treasury balances. Apply regime change: invalidate normal-period correlations. Observe top-account share and correlation. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is relationship retention and liquidity buffer. The failure condition is that one decision creates a cliff. The systems lesson is that historical averages understate nonlinear stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 21: how rapid withdrawal travels through unsecured wholesale funding

Start with the role of unsecured wholesale funding: market confidence-sensitive debt. Shock the node by rapid withdrawal, which can compress the funding clock. Measure rollover probability and spread, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through alternative funding and asset shrinkage. If instead maturities arrive during market closure, the node becomes a transmitter. Remember that time is the first constraint. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 22: feedback test for unsecured wholesale funding

Treat unsecured wholesale funding as a network component rather than an isolated balance-sheet line. Its system function is market confidence-sensitive debt. Under loss revelation, change beliefs about asset value. Track rollover probability and spread and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether alternative funding and asset shrinkage; contagion appears when maturities arrive during market closure. Because information becomes funding risk, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 23: second-round effects from unsecured wholesale funding

unsecured wholesale funding provide market confidence-sensitive debt. After market-price gap, reduce collateral and capital values. Measure rollover probability and spread before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires alternative funding and asset shrinkage. When maturities arrive during market closure, the shock becomes contagious. The core insight is that valuation becomes liquidity. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 24: unsecured wholesale funding under haircut increase

unsecured wholesale funding are modelled here as market confidence-sensitive debt. Apply haircut increase: lower secured funding capacity. Observe rollover probability and spread. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is alternative funding and asset shrinkage. The failure condition is that maturities arrive during market closure. The systems lesson is that collateral rules amplify price stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 25: how margin spike travels through unsecured wholesale funding

Start with the role of unsecured wholesale funding: market confidence-sensitive debt. Shock the node by margin spike, which can create same-day cash demand. Measure rollover probability and spread, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through alternative funding and asset shrinkage. If instead maturities arrive during market closure, the node becomes a transmitter. Remember that risk transfer becomes liquidity demand. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 26: feedback test for unsecured wholesale funding

Treat unsecured wholesale funding as a network component rather than an isolated balance-sheet line. Its system function is market confidence-sensitive debt. Under wholesale closure, remove refinancing channels. Track rollover probability and spread and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether alternative funding and asset shrinkage; contagion appears when maturities arrive during market closure. Because maturity transformation is exposed, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 27: second-round effects from unsecured wholesale funding

unsecured wholesale funding provide market confidence-sensitive debt. After payment outage, delay settlement and create uncertainty. Measure rollover probability and spread before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires alternative funding and asset shrinkage. When maturities arrive during market closure, the shock becomes contagious. The core insight is that operations become finance. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 28: unsecured wholesale funding under counterparty default

unsecured wholesale funding are modelled here as market confidence-sensitive debt. Apply counterparty default: create direct loss and replacement need. Observe rollover probability and spread. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is alternative funding and asset shrinkage. The failure condition is that maturities arrive during market closure. The systems lesson is that network claims transmit stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 29: how rating downgrade travels through unsecured wholesale funding

Start with the role of unsecured wholesale funding: market confidence-sensitive debt. Shock the node by rating downgrade, which can raise spreads and collateral requirements. Measure rollover probability and spread, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through alternative funding and asset shrinkage. If instead maturities arrive during market closure, the node becomes a transmitter. Remember that external classification changes behaviour. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 30: feedback test for unsecured wholesale funding

Treat unsecured wholesale funding as a network component rather than an isolated balance-sheet line. Its system function is market confidence-sensitive debt. Under regime change, invalidate normal-period correlations. Track rollover probability and spread and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether alternative funding and asset shrinkage; contagion appears when maturities arrive during market closure. Because historical averages understate nonlinear stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 31: second-round effects from repo funding

repo funding provide secured short-term borrowing. After rapid withdrawal, compress the funding clock. Measure haircuts, collateral value and tenor before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires collateral substitution and central-bank access. When haircuts and price moves reinforce, the shock becomes contagious. The core insight is that time is the first constraint. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 32: repo funding under loss revelation

repo funding are modelled here as secured short-term borrowing. Apply loss revelation: change beliefs about asset value. Observe haircuts, collateral value and tenor. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is collateral substitution and central-bank access. The failure condition is that haircuts and price moves reinforce. The systems lesson is that information becomes funding risk. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 33: how market-price gap travels through repo funding

Start with the role of repo funding: secured short-term borrowing. Shock the node by market-price gap, which can reduce collateral and capital values. Measure haircuts, collateral value and tenor, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through collateral substitution and central-bank access. If instead haircuts and price moves reinforce, the node becomes a transmitter. Remember that valuation becomes liquidity. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 34: feedback test for repo funding

Treat repo funding as a network component rather than an isolated balance-sheet line. Its system function is secured short-term borrowing. Under haircut increase, lower secured funding capacity. Track haircuts, collateral value and tenor and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether collateral substitution and central-bank access; contagion appears when haircuts and price moves reinforce. Because collateral rules amplify price stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 35: second-round effects from repo funding

repo funding provide secured short-term borrowing. After margin spike, create same-day cash demand. Measure haircuts, collateral value and tenor before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires collateral substitution and central-bank access. When haircuts and price moves reinforce, the shock becomes contagious. The core insight is that risk transfer becomes liquidity demand. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 36: repo funding under wholesale closure

repo funding are modelled here as secured short-term borrowing. Apply wholesale closure: remove refinancing channels. Observe haircuts, collateral value and tenor. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is collateral substitution and central-bank access. The failure condition is that haircuts and price moves reinforce. The systems lesson is that maturity transformation is exposed. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 37: how payment outage travels through repo funding

Start with the role of repo funding: secured short-term borrowing. Shock the node by payment outage, which can delay settlement and create uncertainty. Measure haircuts, collateral value and tenor, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through collateral substitution and central-bank access. If instead haircuts and price moves reinforce, the node becomes a transmitter. Remember that operations become finance. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 38: feedback test for repo funding

Treat repo funding as a network component rather than an isolated balance-sheet line. Its system function is secured short-term borrowing. Under counterparty default, create direct loss and replacement need. Track haircuts, collateral value and tenor and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether collateral substitution and central-bank access; contagion appears when haircuts and price moves reinforce. Because network claims transmit stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 39: second-round effects from repo funding

repo funding provide secured short-term borrowing. After rating downgrade, raise spreads and collateral requirements. Measure haircuts, collateral value and tenor before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires collateral substitution and central-bank access. When haircuts and price moves reinforce, the shock becomes contagious. The core insight is that external classification changes behaviour. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 40: repo funding under regime change

repo funding are modelled here as secured short-term borrowing. Apply regime change: invalidate normal-period correlations. Observe haircuts, collateral value and tenor. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is collateral substitution and central-bank access. The failure condition is that haircuts and price moves reinforce. The systems lesson is that historical averages understate nonlinear stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 41: how rapid withdrawal travels through high-quality liquid assets

Start with the role of high-quality liquid assets: primary liquidity buffer. Shock the node by rapid withdrawal, which can compress the funding clock. Measure sale depth, haircut and encumbrance, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through sale or pledge. If instead buffer is not operationally usable, the node becomes a transmitter. Remember that time is the first constraint. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 42: feedback test for high-quality liquid assets

Treat high-quality liquid assets as a network component rather than an isolated balance-sheet line. Its system function is primary liquidity buffer. Under loss revelation, change beliefs about asset value. Track sale depth, haircut and encumbrance and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether sale or pledge; contagion appears when buffer is not operationally usable. Because information becomes funding risk, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 43: second-round effects from high-quality liquid assets

high-quality liquid assets provide primary liquidity buffer. After market-price gap, reduce collateral and capital values. Measure sale depth, haircut and encumbrance before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires sale or pledge. When buffer is not operationally usable, the shock becomes contagious. The core insight is that valuation becomes liquidity. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 44: high-quality liquid assets under haircut increase

high-quality liquid assets are modelled here as primary liquidity buffer. Apply haircut increase: lower secured funding capacity. Observe sale depth, haircut and encumbrance. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is sale or pledge. The failure condition is that buffer is not operationally usable. The systems lesson is that collateral rules amplify price stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 45: how margin spike travels through high-quality liquid assets

Start with the role of high-quality liquid assets: primary liquidity buffer. Shock the node by margin spike, which can create same-day cash demand. Measure sale depth, haircut and encumbrance, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through sale or pledge. If instead buffer is not operationally usable, the node becomes a transmitter. Remember that risk transfer becomes liquidity demand. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 46: feedback test for high-quality liquid assets

Treat high-quality liquid assets as a network component rather than an isolated balance-sheet line. Its system function is primary liquidity buffer. Under wholesale closure, remove refinancing channels. Track sale depth, haircut and encumbrance and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether sale or pledge; contagion appears when buffer is not operationally usable. Because maturity transformation is exposed, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 47: second-round effects from high-quality liquid assets

high-quality liquid assets provide primary liquidity buffer. After payment outage, delay settlement and create uncertainty. Measure sale depth, haircut and encumbrance before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires sale or pledge. When buffer is not operationally usable, the shock becomes contagious. The core insight is that operations become finance. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 48: high-quality liquid assets under counterparty default

high-quality liquid assets are modelled here as primary liquidity buffer. Apply counterparty default: create direct loss and replacement need. Observe sale depth, haircut and encumbrance. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is sale or pledge. The failure condition is that buffer is not operationally usable. The systems lesson is that network claims transmit stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 49: how rating downgrade travels through high-quality liquid assets

Start with the role of high-quality liquid assets: primary liquidity buffer. Shock the node by rating downgrade, which can raise spreads and collateral requirements. Measure sale depth, haircut and encumbrance, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through sale or pledge. If instead buffer is not operationally usable, the node becomes a transmitter. Remember that external classification changes behaviour. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 50: feedback test for high-quality liquid assets

Treat high-quality liquid assets as a network component rather than an isolated balance-sheet line. Its system function is primary liquidity buffer. Under regime change, invalidate normal-period correlations. Track sale depth, haircut and encumbrance and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether sale or pledge; contagion appears when buffer is not operationally usable. Because historical averages understate nonlinear stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 51: second-round effects from long-duration securities

long-duration securities provide rate-sensitive assets. After rapid withdrawal, compress the funding clock. Measure duration and unrealised loss before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires hedge, hold or sell. When sale crystallises large losses, the shock becomes contagious. The core insight is that time is the first constraint. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 52: long-duration securities under loss revelation

long-duration securities are modelled here as rate-sensitive assets. Apply loss revelation: change beliefs about asset value. Observe duration and unrealised loss. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is hedge, hold or sell. The failure condition is that sale crystallises large losses. The systems lesson is that information becomes funding risk. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 53: how market-price gap travels through long-duration securities

Start with the role of long-duration securities: rate-sensitive assets. Shock the node by market-price gap, which can reduce collateral and capital values. Measure duration and unrealised loss, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through hedge, hold or sell. If instead sale crystallises large losses, the node becomes a transmitter. Remember that valuation becomes liquidity. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 54: feedback test for long-duration securities

Treat long-duration securities as a network component rather than an isolated balance-sheet line. Its system function is rate-sensitive assets. Under haircut increase, lower secured funding capacity. Track duration and unrealised loss and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether hedge, hold or sell; contagion appears when sale crystallises large losses. Because collateral rules amplify price stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 55: second-round effects from long-duration securities

long-duration securities provide rate-sensitive assets. After margin spike, create same-day cash demand. Measure duration and unrealised loss before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires hedge, hold or sell. When sale crystallises large losses, the shock becomes contagious. The core insight is that risk transfer becomes liquidity demand. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 56: long-duration securities under wholesale closure

long-duration securities are modelled here as rate-sensitive assets. Apply wholesale closure: remove refinancing channels. Observe duration and unrealised loss. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is hedge, hold or sell. The failure condition is that sale crystallises large losses. The systems lesson is that maturity transformation is exposed. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 57: how payment outage travels through long-duration securities

Start with the role of long-duration securities: rate-sensitive assets. Shock the node by payment outage, which can delay settlement and create uncertainty. Measure duration and unrealised loss, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through hedge, hold or sell. If instead sale crystallises large losses, the node becomes a transmitter. Remember that operations become finance. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 58: feedback test for long-duration securities

Treat long-duration securities as a network component rather than an isolated balance-sheet line. Its system function is rate-sensitive assets. Under counterparty default, create direct loss and replacement need. Track duration and unrealised loss and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether hedge, hold or sell; contagion appears when sale crystallises large losses. Because network claims transmit stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 59: second-round effects from long-duration securities

long-duration securities provide rate-sensitive assets. After rating downgrade, raise spreads and collateral requirements. Measure duration and unrealised loss before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires hedge, hold or sell. When sale crystallises large losses, the shock becomes contagious. The core insight is that external classification changes behaviour. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 60: long-duration securities under regime change

long-duration securities are modelled here as rate-sensitive assets. Apply regime change: invalidate normal-period correlations. Observe duration and unrealised loss. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is hedge, hold or sell. The failure condition is that sale crystallises large losses. The systems lesson is that historical averages understate nonlinear stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 61: how rapid withdrawal travels through loan books

Start with the role of loan books: illiquid earning assets. Shock the node by rapid withdrawal, which can compress the funding clock. Measure credit loss and sale discount, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through runoff, securitisation or sale. If instead cash need arrives before natural repayment, the node becomes a transmitter. Remember that time is the first constraint. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 62: feedback test for loan books

Treat loan books as a network component rather than an isolated balance-sheet line. Its system function is illiquid earning assets. Under loss revelation, change beliefs about asset value. Track credit loss and sale discount and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether runoff, securitisation or sale; contagion appears when cash need arrives before natural repayment. Because information becomes funding risk, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 63: second-round effects from loan books

loan books provide illiquid earning assets. After market-price gap, reduce collateral and capital values. Measure credit loss and sale discount before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires runoff, securitisation or sale. When cash need arrives before natural repayment, the shock becomes contagious. The core insight is that valuation becomes liquidity. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 64: loan books under haircut increase

loan books are modelled here as illiquid earning assets. Apply haircut increase: lower secured funding capacity. Observe credit loss and sale discount. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is runoff, securitisation or sale. The failure condition is that cash need arrives before natural repayment. The systems lesson is that collateral rules amplify price stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 65: how margin spike travels through loan books

Start with the role of loan books: illiquid earning assets. Shock the node by margin spike, which can create same-day cash demand. Measure credit loss and sale discount, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through runoff, securitisation or sale. If instead cash need arrives before natural repayment, the node becomes a transmitter. Remember that risk transfer becomes liquidity demand. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 66: feedback test for loan books

Treat loan books as a network component rather than an isolated balance-sheet line. Its system function is illiquid earning assets. Under wholesale closure, remove refinancing channels. Track credit loss and sale discount and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether runoff, securitisation or sale; contagion appears when cash need arrives before natural repayment. Because maturity transformation is exposed, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 67: second-round effects from loan books

loan books provide illiquid earning assets. After payment outage, delay settlement and create uncertainty. Measure credit loss and sale discount before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires runoff, securitisation or sale. When cash need arrives before natural repayment, the shock becomes contagious. The core insight is that operations become finance. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 68: loan books under counterparty default

loan books are modelled here as illiquid earning assets. Apply counterparty default: create direct loss and replacement need. Observe credit loss and sale discount. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is runoff, securitisation or sale. The failure condition is that cash need arrives before natural repayment. The systems lesson is that network claims transmit stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 69: how rating downgrade travels through loan books

Start with the role of loan books: illiquid earning assets. Shock the node by rating downgrade, which can raise spreads and collateral requirements. Measure credit loss and sale discount, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through runoff, securitisation or sale. If instead cash need arrives before natural repayment, the node becomes a transmitter. Remember that external classification changes behaviour. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 70: feedback test for loan books

Treat loan books as a network component rather than an isolated balance-sheet line. Its system function is illiquid earning assets. Under regime change, invalidate normal-period correlations. Track credit loss and sale discount and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether runoff, securitisation or sale; contagion appears when cash need arrives before natural repayment. Because historical averages understate nonlinear stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 71: second-round effects from derivative positions

derivative positions provide market-risk and collateral exposures. After rapid withdrawal, compress the funding clock. Measure variation margin and netting before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires hedges and collateral. When margin creates immediate cash need, the shock becomes contagious. The core insight is that time is the first constraint. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 72: derivative positions under loss revelation

derivative positions are modelled here as market-risk and collateral exposures. Apply loss revelation: change beliefs about asset value. Observe variation margin and netting. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is hedges and collateral. The failure condition is that margin creates immediate cash need. The systems lesson is that information becomes funding risk. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 73: how market-price gap travels through derivative positions

Start with the role of derivative positions: market-risk and collateral exposures. Shock the node by market-price gap, which can reduce collateral and capital values. Measure variation margin and netting, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through hedges and collateral. If instead margin creates immediate cash need, the node becomes a transmitter. Remember that valuation becomes liquidity. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 74: feedback test for derivative positions

Treat derivative positions as a network component rather than an isolated balance-sheet line. Its system function is market-risk and collateral exposures. Under haircut increase, lower secured funding capacity. Track variation margin and netting and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether hedges and collateral; contagion appears when margin creates immediate cash need. Because collateral rules amplify price stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 75: second-round effects from derivative positions

derivative positions provide market-risk and collateral exposures. After margin spike, create same-day cash demand. Measure variation margin and netting before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires hedges and collateral. When margin creates immediate cash need, the shock becomes contagious. The core insight is that risk transfer becomes liquidity demand. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 76: derivative positions under wholesale closure

derivative positions are modelled here as market-risk and collateral exposures. Apply wholesale closure: remove refinancing channels. Observe variation margin and netting. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is hedges and collateral. The failure condition is that margin creates immediate cash need. The systems lesson is that maturity transformation is exposed. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 77: how payment outage travels through derivative positions

Start with the role of derivative positions: market-risk and collateral exposures. Shock the node by payment outage, which can delay settlement and create uncertainty. Measure variation margin and netting, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through hedges and collateral. If instead margin creates immediate cash need, the node becomes a transmitter. Remember that operations become finance. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 78: feedback test for derivative positions

Treat derivative positions as a network component rather than an isolated balance-sheet line. Its system function is market-risk and collateral exposures. Under counterparty default, create direct loss and replacement need. Track variation margin and netting and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether hedges and collateral; contagion appears when margin creates immediate cash need. Because network claims transmit stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 79: second-round effects from derivative positions

derivative positions provide market-risk and collateral exposures. After rating downgrade, raise spreads and collateral requirements. Measure variation margin and netting before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires hedges and collateral. When margin creates immediate cash need, the shock becomes contagious. The core insight is that external classification changes behaviour. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 80: derivative positions under regime change

derivative positions are modelled here as market-risk and collateral exposures. Apply regime change: invalidate normal-period correlations. Observe variation margin and netting. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is hedges and collateral. The failure condition is that margin creates immediate cash need. The systems lesson is that historical averages understate nonlinear stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 81: how rapid withdrawal travels through central counterparties

Start with the role of central counterparties: clearing hubs. Shock the node by rapid withdrawal, which can compress the funding clock. Measure margin, default fund and participant concentration, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through default management. If instead liquidity calls cluster, the node becomes a transmitter. Remember that time is the first constraint. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 82: feedback test for central counterparties

Treat central counterparties as a network component rather than an isolated balance-sheet line. Its system function is clearing hubs. Under loss revelation, change beliefs about asset value. Track margin, default fund and participant concentration and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether default management; contagion appears when liquidity calls cluster. Because information becomes funding risk, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 83: second-round effects from central counterparties

central counterparties provide clearing hubs. After market-price gap, reduce collateral and capital values. Measure margin, default fund and participant concentration before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires default management. When liquidity calls cluster, the shock becomes contagious. The core insight is that valuation becomes liquidity. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 84: central counterparties under haircut increase

central counterparties are modelled here as clearing hubs. Apply haircut increase: lower secured funding capacity. Observe margin, default fund and participant concentration. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is default management. The failure condition is that liquidity calls cluster. The systems lesson is that collateral rules amplify price stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 85: how margin spike travels through central counterparties

Start with the role of central counterparties: clearing hubs. Shock the node by margin spike, which can create same-day cash demand. Measure margin, default fund and participant concentration, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through default management. If instead liquidity calls cluster, the node becomes a transmitter. Remember that risk transfer becomes liquidity demand. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 86: feedback test for central counterparties

Treat central counterparties as a network component rather than an isolated balance-sheet line. Its system function is clearing hubs. Under wholesale closure, remove refinancing channels. Track margin, default fund and participant concentration and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether default management; contagion appears when liquidity calls cluster. Because maturity transformation is exposed, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 87: second-round effects from central counterparties

central counterparties provide clearing hubs. After payment outage, delay settlement and create uncertainty. Measure margin, default fund and participant concentration before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires default management. When liquidity calls cluster, the shock becomes contagious. The core insight is that operations become finance. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 88: central counterparties under counterparty default

central counterparties are modelled here as clearing hubs. Apply counterparty default: create direct loss and replacement need. Observe margin, default fund and participant concentration. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is default management. The failure condition is that liquidity calls cluster. The systems lesson is that network claims transmit stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 89: how rating downgrade travels through central counterparties

Start with the role of central counterparties: clearing hubs. Shock the node by rating downgrade, which can raise spreads and collateral requirements. Measure margin, default fund and participant concentration, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through default management. If instead liquidity calls cluster, the node becomes a transmitter. Remember that external classification changes behaviour. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 90: feedback test for central counterparties

Treat central counterparties as a network component rather than an isolated balance-sheet line. Its system function is clearing hubs. Under regime change, invalidate normal-period correlations. Track margin, default fund and participant concentration and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether default management; contagion appears when liquidity calls cluster. Because historical averages understate nonlinear stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 91: second-round effects from investment funds

investment funds provide redeemable portfolios. After rapid withdrawal, compress the funding clock. Measure redemption and market liquidity before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires cash buffer or asset sale. When redemptions force common-asset sales, the shock becomes contagious. The core insight is that time is the first constraint. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 92: investment funds under loss revelation

investment funds are modelled here as redeemable portfolios. Apply loss revelation: change beliefs about asset value. Observe redemption and market liquidity. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is cash buffer or asset sale. The failure condition is that redemptions force common-asset sales. The systems lesson is that information becomes funding risk. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 93: how market-price gap travels through investment funds

Start with the role of investment funds: redeemable portfolios. Shock the node by market-price gap, which can reduce collateral and capital values. Measure redemption and market liquidity, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through cash buffer or asset sale. If instead redemptions force common-asset sales, the node becomes a transmitter. Remember that valuation becomes liquidity. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 94: feedback test for investment funds

Treat investment funds as a network component rather than an isolated balance-sheet line. Its system function is redeemable portfolios. Under haircut increase, lower secured funding capacity. Track redemption and market liquidity and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether cash buffer or asset sale; contagion appears when redemptions force common-asset sales. Because collateral rules amplify price stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 95: second-round effects from investment funds

investment funds provide redeemable portfolios. After margin spike, create same-day cash demand. Measure redemption and market liquidity before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires cash buffer or asset sale. When redemptions force common-asset sales, the shock becomes contagious. The core insight is that risk transfer becomes liquidity demand. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 96: investment funds under wholesale closure

investment funds are modelled here as redeemable portfolios. Apply wholesale closure: remove refinancing channels. Observe redemption and market liquidity. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is cash buffer or asset sale. The failure condition is that redemptions force common-asset sales. The systems lesson is that maturity transformation is exposed. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 97: how payment outage travels through investment funds

Start with the role of investment funds: redeemable portfolios. Shock the node by payment outage, which can delay settlement and create uncertainty. Measure redemption and market liquidity, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through cash buffer or asset sale. If instead redemptions force common-asset sales, the node becomes a transmitter. Remember that operations become finance. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 98: feedback test for investment funds

Treat investment funds as a network component rather than an isolated balance-sheet line. Its system function is redeemable portfolios. Under counterparty default, create direct loss and replacement need. Track redemption and market liquidity and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether cash buffer or asset sale; contagion appears when redemptions force common-asset sales. Because network claims transmit stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 99: second-round effects from investment funds

investment funds provide redeemable portfolios. After rating downgrade, raise spreads and collateral requirements. Measure redemption and market liquidity before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires cash buffer or asset sale. When redemptions force common-asset sales, the shock becomes contagious. The core insight is that external classification changes behaviour. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 100: investment funds under regime change

investment funds are modelled here as redeemable portfolios. Apply regime change: invalidate normal-period correlations. Observe redemption and market liquidity. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is cash buffer or asset sale. The failure condition is that redemptions force common-asset sales. The systems lesson is that historical averages understate nonlinear stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 101: how rapid withdrawal travels through money-market funds

Start with the role of money-market funds: short-duration pooled vehicles. Shock the node by rapid withdrawal, which can compress the funding clock. Measure redemption, liquidity and asset quality, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through liquidity tools under applicable rules. If instead investor run changes short-term funding markets, the node becomes a transmitter. Remember that time is the first constraint. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 102: feedback test for money-market funds

Treat money-market funds as a network component rather than an isolated balance-sheet line. Its system function is short-duration pooled vehicles. Under loss revelation, change beliefs about asset value. Track redemption, liquidity and asset quality and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether liquidity tools under applicable rules; contagion appears when investor run changes short-term funding markets. Because information becomes funding risk, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 103: second-round effects from money-market funds

money-market funds provide short-duration pooled vehicles. After market-price gap, reduce collateral and capital values. Measure redemption, liquidity and asset quality before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires liquidity tools under applicable rules. When investor run changes short-term funding markets, the shock becomes contagious. The core insight is that valuation becomes liquidity. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 104: money-market funds under haircut increase

money-market funds are modelled here as short-duration pooled vehicles. Apply haircut increase: lower secured funding capacity. Observe redemption, liquidity and asset quality. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is liquidity tools under applicable rules. The failure condition is that investor run changes short-term funding markets. The systems lesson is that collateral rules amplify price stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 105: how margin spike travels through money-market funds

Start with the role of money-market funds: short-duration pooled vehicles. Shock the node by margin spike, which can create same-day cash demand. Measure redemption, liquidity and asset quality, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through liquidity tools under applicable rules. If instead investor run changes short-term funding markets, the node becomes a transmitter. Remember that risk transfer becomes liquidity demand. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 106: feedback test for money-market funds

Treat money-market funds as a network component rather than an isolated balance-sheet line. Its system function is short-duration pooled vehicles. Under wholesale closure, remove refinancing channels. Track redemption, liquidity and asset quality and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether liquidity tools under applicable rules; contagion appears when investor run changes short-term funding markets. Because maturity transformation is exposed, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 107: second-round effects from money-market funds

money-market funds provide short-duration pooled vehicles. After payment outage, delay settlement and create uncertainty. Measure redemption, liquidity and asset quality before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires liquidity tools under applicable rules. When investor run changes short-term funding markets, the shock becomes contagious. The core insight is that operations become finance. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 108: money-market funds under counterparty default

money-market funds are modelled here as short-duration pooled vehicles. Apply counterparty default: create direct loss and replacement need. Observe redemption, liquidity and asset quality. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is liquidity tools under applicable rules. The failure condition is that investor run changes short-term funding markets. The systems lesson is that network claims transmit stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 109: how rating downgrade travels through money-market funds

Start with the role of money-market funds: short-duration pooled vehicles. Shock the node by rating downgrade, which can raise spreads and collateral requirements. Measure redemption, liquidity and asset quality, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through liquidity tools under applicable rules. If instead investor run changes short-term funding markets, the node becomes a transmitter. Remember that external classification changes behaviour. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 110: feedback test for money-market funds

Treat money-market funds as a network component rather than an isolated balance-sheet line. Its system function is short-duration pooled vehicles. Under regime change, invalidate normal-period correlations. Track redemption, liquidity and asset quality and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether liquidity tools under applicable rules; contagion appears when investor run changes short-term funding markets. Because historical averages understate nonlinear stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 111: second-round effects from insurers

insurers provide long-horizon liabilities with market exposures. After rapid withdrawal, compress the funding clock. Measure collateral calls and asset sales before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires liquidity pools and asset allocation. When derivative or policy cash needs spike, the shock becomes contagious. The core insight is that time is the first constraint. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 112: insurers under loss revelation

insurers are modelled here as long-horizon liabilities with market exposures. Apply loss revelation: change beliefs about asset value. Observe collateral calls and asset sales. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is liquidity pools and asset allocation. The failure condition is that derivative or policy cash needs spike. The systems lesson is that information becomes funding risk. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 113: how market-price gap travels through insurers

Start with the role of insurers: long-horizon liabilities with market exposures. Shock the node by market-price gap, which can reduce collateral and capital values. Measure collateral calls and asset sales, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through liquidity pools and asset allocation. If instead derivative or policy cash needs spike, the node becomes a transmitter. Remember that valuation becomes liquidity. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 114: feedback test for insurers

Treat insurers as a network component rather than an isolated balance-sheet line. Its system function is long-horizon liabilities with market exposures. Under haircut increase, lower secured funding capacity. Track collateral calls and asset sales and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether liquidity pools and asset allocation; contagion appears when derivative or policy cash needs spike. Because collateral rules amplify price stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 115: second-round effects from insurers

insurers provide long-horizon liabilities with market exposures. After margin spike, create same-day cash demand. Measure collateral calls and asset sales before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires liquidity pools and asset allocation. When derivative or policy cash needs spike, the shock becomes contagious. The core insight is that risk transfer becomes liquidity demand. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 116: insurers under wholesale closure

insurers are modelled here as long-horizon liabilities with market exposures. Apply wholesale closure: remove refinancing channels. Observe collateral calls and asset sales. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is liquidity pools and asset allocation. The failure condition is that derivative or policy cash needs spike. The systems lesson is that maturity transformation is exposed. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 117: how payment outage travels through insurers

Start with the role of insurers: long-horizon liabilities with market exposures. Shock the node by payment outage, which can delay settlement and create uncertainty. Measure collateral calls and asset sales, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through liquidity pools and asset allocation. If instead derivative or policy cash needs spike, the node becomes a transmitter. Remember that operations become finance. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 118: feedback test for insurers

Treat insurers as a network component rather than an isolated balance-sheet line. Its system function is long-horizon liabilities with market exposures. Under counterparty default, create direct loss and replacement need. Track collateral calls and asset sales and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether liquidity pools and asset allocation; contagion appears when derivative or policy cash needs spike. Because network claims transmit stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 119: second-round effects from insurers

insurers provide long-horizon liabilities with market exposures. After rating downgrade, raise spreads and collateral requirements. Measure collateral calls and asset sales before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires liquidity pools and asset allocation. When derivative or policy cash needs spike, the shock becomes contagious. The core insight is that external classification changes behaviour. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 120: insurers under regime change

insurers are modelled here as long-horizon liabilities with market exposures. Apply regime change: invalidate normal-period correlations. Observe collateral calls and asset sales. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is liquidity pools and asset allocation. The failure condition is that derivative or policy cash needs spike. The systems lesson is that historical averages understate nonlinear stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 121: how rapid withdrawal travels through hedge funds

Start with the role of hedge funds: leveraged market participants. Shock the node by rapid withdrawal, which can compress the funding clock. Measure margin, repo and prime-broker terms, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through deleverage or raise cash. If instead forced unwind moves market prices, the node becomes a transmitter. Remember that time is the first constraint. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 122: feedback test for hedge funds

Treat hedge funds as a network component rather than an isolated balance-sheet line. Its system function is leveraged market participants. Under loss revelation, change beliefs about asset value. Track margin, repo and prime-broker terms and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether deleverage or raise cash; contagion appears when forced unwind moves market prices. Because information becomes funding risk, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 123: second-round effects from hedge funds

hedge funds provide leveraged market participants. After market-price gap, reduce collateral and capital values. Measure margin, repo and prime-broker terms before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires deleverage or raise cash. When forced unwind moves market prices, the shock becomes contagious. The core insight is that valuation becomes liquidity. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 124: hedge funds under haircut increase

hedge funds are modelled here as leveraged market participants. Apply haircut increase: lower secured funding capacity. Observe margin, repo and prime-broker terms. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is deleverage or raise cash. The failure condition is that forced unwind moves market prices. The systems lesson is that collateral rules amplify price stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 125: how margin spike travels through hedge funds

Start with the role of hedge funds: leveraged market participants. Shock the node by margin spike, which can create same-day cash demand. Measure margin, repo and prime-broker terms, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through deleverage or raise cash. If instead forced unwind moves market prices, the node becomes a transmitter. Remember that risk transfer becomes liquidity demand. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 126: feedback test for hedge funds

Treat hedge funds as a network component rather than an isolated balance-sheet line. Its system function is leveraged market participants. Under wholesale closure, remove refinancing channels. Track margin, repo and prime-broker terms and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether deleverage or raise cash; contagion appears when forced unwind moves market prices. Because maturity transformation is exposed, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 127: second-round effects from hedge funds

hedge funds provide leveraged market participants. After payment outage, delay settlement and create uncertainty. Measure margin, repo and prime-broker terms before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires deleverage or raise cash. When forced unwind moves market prices, the shock becomes contagious. The core insight is that operations become finance. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 128: hedge funds under counterparty default

hedge funds are modelled here as leveraged market participants. Apply counterparty default: create direct loss and replacement need. Observe margin, repo and prime-broker terms. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is deleverage or raise cash. The failure condition is that forced unwind moves market prices. The systems lesson is that network claims transmit stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 129: how rating downgrade travels through hedge funds

Start with the role of hedge funds: leveraged market participants. Shock the node by rating downgrade, which can raise spreads and collateral requirements. Measure margin, repo and prime-broker terms, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through deleverage or raise cash. If instead forced unwind moves market prices, the node becomes a transmitter. Remember that external classification changes behaviour. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 130: feedback test for hedge funds

Treat hedge funds as a network component rather than an isolated balance-sheet line. Its system function is leveraged market participants. Under regime change, invalidate normal-period correlations. Track margin, repo and prime-broker terms and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether deleverage or raise cash; contagion appears when forced unwind moves market prices. Because historical averages understate nonlinear stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 131: second-round effects from dealers

dealers provide market-making intermediaries. After rapid withdrawal, compress the funding clock. Measure inventory, balance-sheet capacity and spreads before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires provide or withdraw liquidity. When intermediation capacity shrinks in stress, the shock becomes contagious. The core insight is that time is the first constraint. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 132: dealers under loss revelation

dealers are modelled here as market-making intermediaries. Apply loss revelation: change beliefs about asset value. Observe inventory, balance-sheet capacity and spreads. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is provide or withdraw liquidity. The failure condition is that intermediation capacity shrinks in stress. The systems lesson is that information becomes funding risk. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 133: how market-price gap travels through dealers

Start with the role of dealers: market-making intermediaries. Shock the node by market-price gap, which can reduce collateral and capital values. Measure inventory, balance-sheet capacity and spreads, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through provide or withdraw liquidity. If instead intermediation capacity shrinks in stress, the node becomes a transmitter. Remember that valuation becomes liquidity. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 134: feedback test for dealers

Treat dealers as a network component rather than an isolated balance-sheet line. Its system function is market-making intermediaries. Under haircut increase, lower secured funding capacity. Track inventory, balance-sheet capacity and spreads and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether provide or withdraw liquidity; contagion appears when intermediation capacity shrinks in stress. Because collateral rules amplify price stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 135: second-round effects from dealers

dealers provide market-making intermediaries. After margin spike, create same-day cash demand. Measure inventory, balance-sheet capacity and spreads before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires provide or withdraw liquidity. When intermediation capacity shrinks in stress, the shock becomes contagious. The core insight is that risk transfer becomes liquidity demand. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 136: dealers under wholesale closure

dealers are modelled here as market-making intermediaries. Apply wholesale closure: remove refinancing channels. Observe inventory, balance-sheet capacity and spreads. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is provide or withdraw liquidity. The failure condition is that intermediation capacity shrinks in stress. The systems lesson is that maturity transformation is exposed. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 137: how payment outage travels through dealers

Start with the role of dealers: market-making intermediaries. Shock the node by payment outage, which can delay settlement and create uncertainty. Measure inventory, balance-sheet capacity and spreads, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through provide or withdraw liquidity. If instead intermediation capacity shrinks in stress, the node becomes a transmitter. Remember that operations become finance. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 138: feedback test for dealers

Treat dealers as a network component rather than an isolated balance-sheet line. Its system function is market-making intermediaries. Under counterparty default, create direct loss and replacement need. Track inventory, balance-sheet capacity and spreads and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether provide or withdraw liquidity; contagion appears when intermediation capacity shrinks in stress. Because network claims transmit stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 139: second-round effects from dealers

dealers provide market-making intermediaries. After rating downgrade, raise spreads and collateral requirements. Measure inventory, balance-sheet capacity and spreads before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires provide or withdraw liquidity. When intermediation capacity shrinks in stress, the shock becomes contagious. The core insight is that external classification changes behaviour. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 140: dealers under regime change

dealers are modelled here as market-making intermediaries. Apply regime change: invalidate normal-period correlations. Observe inventory, balance-sheet capacity and spreads. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is provide or withdraw liquidity. The failure condition is that intermediation capacity shrinks in stress. The systems lesson is that historical averages understate nonlinear stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 141: how rapid withdrawal travels through payment systems

Start with the role of payment systems: settlement infrastructure. Shock the node by rapid withdrawal, which can compress the funding clock. Measure queue, throughput and participant liquidity, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through liquidity-saving mechanisms. If instead gridlock amplifies bank stress, the node becomes a transmitter. Remember that time is the first constraint. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 142: feedback test for payment systems

Treat payment systems as a network component rather than an isolated balance-sheet line. Its system function is settlement infrastructure. Under loss revelation, change beliefs about asset value. Track queue, throughput and participant liquidity and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether liquidity-saving mechanisms; contagion appears when gridlock amplifies bank stress. Because information becomes funding risk, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 143: second-round effects from payment systems

payment systems provide settlement infrastructure. After market-price gap, reduce collateral and capital values. Measure queue, throughput and participant liquidity before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires liquidity-saving mechanisms. When gridlock amplifies bank stress, the shock becomes contagious. The core insight is that valuation becomes liquidity. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 144: payment systems under haircut increase

payment systems are modelled here as settlement infrastructure. Apply haircut increase: lower secured funding capacity. Observe queue, throughput and participant liquidity. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is liquidity-saving mechanisms. The failure condition is that gridlock amplifies bank stress. The systems lesson is that collateral rules amplify price stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 145: how margin spike travels through payment systems

Start with the role of payment systems: settlement infrastructure. Shock the node by margin spike, which can create same-day cash demand. Measure queue, throughput and participant liquidity, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through liquidity-saving mechanisms. If instead gridlock amplifies bank stress, the node becomes a transmitter. Remember that risk transfer becomes liquidity demand. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 146: feedback test for payment systems

Treat payment systems as a network component rather than an isolated balance-sheet line. Its system function is settlement infrastructure. Under wholesale closure, remove refinancing channels. Track queue, throughput and participant liquidity and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether liquidity-saving mechanisms; contagion appears when gridlock amplifies bank stress. Because maturity transformation is exposed, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 147: second-round effects from payment systems

payment systems provide settlement infrastructure. After payment outage, delay settlement and create uncertainty. Measure queue, throughput and participant liquidity before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires liquidity-saving mechanisms. When gridlock amplifies bank stress, the shock becomes contagious. The core insight is that operations become finance. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 148: payment systems under counterparty default

payment systems are modelled here as settlement infrastructure. Apply counterparty default: create direct loss and replacement need. Observe queue, throughput and participant liquidity. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is liquidity-saving mechanisms. The failure condition is that gridlock amplifies bank stress. The systems lesson is that network claims transmit stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 149: how rating downgrade travels through payment systems

Start with the role of payment systems: settlement infrastructure. Shock the node by rating downgrade, which can raise spreads and collateral requirements. Measure queue, throughput and participant liquidity, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through liquidity-saving mechanisms. If instead gridlock amplifies bank stress, the node becomes a transmitter. Remember that external classification changes behaviour. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 150: feedback test for payment systems

Treat payment systems as a network component rather than an isolated balance-sheet line. Its system function is settlement infrastructure. Under regime change, invalidate normal-period correlations. Track queue, throughput and participant liquidity and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether liquidity-saving mechanisms; contagion appears when gridlock amplifies bank stress. Because historical averages understate nonlinear stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 151: second-round effects from correspondent banks

correspondent banks provide cross-border payment nodes. After rapid withdrawal, compress the funding clock. Measure nostro balances and network concentration before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires reroute payments. When failure blocks downstream flows, the shock becomes contagious. The core insight is that time is the first constraint. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 152: correspondent banks under loss revelation

correspondent banks are modelled here as cross-border payment nodes. Apply loss revelation: change beliefs about asset value. Observe nostro balances and network concentration. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is reroute payments. The failure condition is that failure blocks downstream flows. The systems lesson is that information becomes funding risk. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 153: how market-price gap travels through correspondent banks

Start with the role of correspondent banks: cross-border payment nodes. Shock the node by market-price gap, which can reduce collateral and capital values. Measure nostro balances and network concentration, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through reroute payments. If instead failure blocks downstream flows, the node becomes a transmitter. Remember that valuation becomes liquidity. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 154: feedback test for correspondent banks

Treat correspondent banks as a network component rather than an isolated balance-sheet line. Its system function is cross-border payment nodes. Under haircut increase, lower secured funding capacity. Track nostro balances and network concentration and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether reroute payments; contagion appears when failure blocks downstream flows. Because collateral rules amplify price stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 155: second-round effects from correspondent banks

correspondent banks provide cross-border payment nodes. After margin spike, create same-day cash demand. Measure nostro balances and network concentration before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires reroute payments. When failure blocks downstream flows, the shock becomes contagious. The core insight is that risk transfer becomes liquidity demand. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 156: correspondent banks under wholesale closure

correspondent banks are modelled here as cross-border payment nodes. Apply wholesale closure: remove refinancing channels. Observe nostro balances and network concentration. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is reroute payments. The failure condition is that failure blocks downstream flows. The systems lesson is that maturity transformation is exposed. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 157: how payment outage travels through correspondent banks

Start with the role of correspondent banks: cross-border payment nodes. Shock the node by payment outage, which can delay settlement and create uncertainty. Measure nostro balances and network concentration, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through reroute payments. If instead failure blocks downstream flows, the node becomes a transmitter. Remember that operations become finance. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 158: feedback test for correspondent banks

Treat correspondent banks as a network component rather than an isolated balance-sheet line. Its system function is cross-border payment nodes. Under counterparty default, create direct loss and replacement need. Track nostro balances and network concentration and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether reroute payments; contagion appears when failure blocks downstream flows. Because network claims transmit stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 159: second-round effects from correspondent banks

correspondent banks provide cross-border payment nodes. After rating downgrade, raise spreads and collateral requirements. Measure nostro balances and network concentration before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires reroute payments. When failure blocks downstream flows, the shock becomes contagious. The core insight is that external classification changes behaviour. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 160: correspondent banks under regime change

correspondent banks are modelled here as cross-border payment nodes. Apply regime change: invalidate normal-period correlations. Observe nostro balances and network concentration. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is reroute payments. The failure condition is that failure blocks downstream flows. The systems lesson is that historical averages understate nonlinear stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 161: how rapid withdrawal travels through custodians

Start with the role of custodians: asset servicing and collateral nodes. Shock the node by rapid withdrawal, which can compress the funding clock. Measure operational availability and asset access, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through fallback arrangements. If instead assets become operationally inaccessible, the node becomes a transmitter. Remember that time is the first constraint. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 162: feedback test for custodians

Treat custodians as a network component rather than an isolated balance-sheet line. Its system function is asset servicing and collateral nodes. Under loss revelation, change beliefs about asset value. Track operational availability and asset access and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether fallback arrangements; contagion appears when assets become operationally inaccessible. Because information becomes funding risk, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 163: second-round effects from custodians

custodians provide asset servicing and collateral nodes. After market-price gap, reduce collateral and capital values. Measure operational availability and asset access before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires fallback arrangements. When assets become operationally inaccessible, the shock becomes contagious. The core insight is that valuation becomes liquidity. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 164: custodians under haircut increase

custodians are modelled here as asset servicing and collateral nodes. Apply haircut increase: lower secured funding capacity. Observe operational availability and asset access. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is fallback arrangements. The failure condition is that assets become operationally inaccessible. The systems lesson is that collateral rules amplify price stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 165: how margin spike travels through custodians

Start with the role of custodians: asset servicing and collateral nodes. Shock the node by margin spike, which can create same-day cash demand. Measure operational availability and asset access, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through fallback arrangements. If instead assets become operationally inaccessible, the node becomes a transmitter. Remember that risk transfer becomes liquidity demand. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 166: feedback test for custodians

Treat custodians as a network component rather than an isolated balance-sheet line. Its system function is asset servicing and collateral nodes. Under wholesale closure, remove refinancing channels. Track operational availability and asset access and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether fallback arrangements; contagion appears when assets become operationally inaccessible. Because maturity transformation is exposed, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 167: second-round effects from custodians

custodians provide asset servicing and collateral nodes. After payment outage, delay settlement and create uncertainty. Measure operational availability and asset access before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires fallback arrangements. When assets become operationally inaccessible, the shock becomes contagious. The core insight is that operations become finance. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 168: custodians under counterparty default

custodians are modelled here as asset servicing and collateral nodes. Apply counterparty default: create direct loss and replacement need. Observe operational availability and asset access. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is fallback arrangements. The failure condition is that assets become operationally inaccessible. The systems lesson is that network claims transmit stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 169: how rating downgrade travels through custodians

Start with the role of custodians: asset servicing and collateral nodes. Shock the node by rating downgrade, which can raise spreads and collateral requirements. Measure operational availability and asset access, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through fallback arrangements. If instead assets become operationally inaccessible, the node becomes a transmitter. Remember that external classification changes behaviour. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 170: feedback test for custodians

Treat custodians as a network component rather than an isolated balance-sheet line. Its system function is asset servicing and collateral nodes. Under regime change, invalidate normal-period correlations. Track operational availability and asset access and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether fallback arrangements; contagion appears when assets become operationally inaccessible. Because historical averages understate nonlinear stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 171: second-round effects from central banks

central banks provide settlement and liquidity backstop institutions. After rapid withdrawal, compress the funding clock. Measure eligible collateral and operational readiness before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires liquidity facilities. When support arrives too late or collateral is insufficient, the shock becomes contagious. The core insight is that time is the first constraint. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 172: central banks under loss revelation

central banks are modelled here as settlement and liquidity backstop institutions. Apply loss revelation: change beliefs about asset value. Observe eligible collateral and operational readiness. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is liquidity facilities. The failure condition is that support arrives too late or collateral is insufficient. The systems lesson is that information becomes funding risk. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 173: how market-price gap travels through central banks

Start with the role of central banks: settlement and liquidity backstop institutions. Shock the node by market-price gap, which can reduce collateral and capital values. Measure eligible collateral and operational readiness, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through liquidity facilities. If instead support arrives too late or collateral is insufficient, the node becomes a transmitter. Remember that valuation becomes liquidity. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 174: feedback test for central banks

Treat central banks as a network component rather than an isolated balance-sheet line. Its system function is settlement and liquidity backstop institutions. Under haircut increase, lower secured funding capacity. Track eligible collateral and operational readiness and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether liquidity facilities; contagion appears when support arrives too late or collateral is insufficient. Because collateral rules amplify price stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 175: second-round effects from central banks

central banks provide settlement and liquidity backstop institutions. After margin spike, create same-day cash demand. Measure eligible collateral and operational readiness before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires liquidity facilities. When support arrives too late or collateral is insufficient, the shock becomes contagious. The core insight is that risk transfer becomes liquidity demand. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 176: central banks under wholesale closure

central banks are modelled here as settlement and liquidity backstop institutions. Apply wholesale closure: remove refinancing channels. Observe eligible collateral and operational readiness. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is liquidity facilities. The failure condition is that support arrives too late or collateral is insufficient. The systems lesson is that maturity transformation is exposed. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 177: how payment outage travels through central banks

Start with the role of central banks: settlement and liquidity backstop institutions. Shock the node by payment outage, which can delay settlement and create uncertainty. Measure eligible collateral and operational readiness, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through liquidity facilities. If instead support arrives too late or collateral is insufficient, the node becomes a transmitter. Remember that operations become finance. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 178: feedback test for central banks

Treat central banks as a network component rather than an isolated balance-sheet line. Its system function is settlement and liquidity backstop institutions. Under counterparty default, create direct loss and replacement need. Track eligible collateral and operational readiness and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether liquidity facilities; contagion appears when support arrives too late or collateral is insufficient. Because network claims transmit stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 179: second-round effects from central banks

central banks provide settlement and liquidity backstop institutions. After rating downgrade, raise spreads and collateral requirements. Measure eligible collateral and operational readiness before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires liquidity facilities. When support arrives too late or collateral is insufficient, the shock becomes contagious. The core insight is that external classification changes behaviour. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 180: central banks under regime change

central banks are modelled here as settlement and liquidity backstop institutions. Apply regime change: invalidate normal-period correlations. Observe eligible collateral and operational readiness. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is liquidity facilities. The failure condition is that support arrives too late or collateral is insufficient. The systems lesson is that historical averages understate nonlinear stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 181: how rapid withdrawal travels through deposit insurers

Start with the role of deposit insurers: failure-loss allocation and depositor protection. Shock the node by rapid withdrawal, which can compress the funding clock. Measure coverage credibility and payout readiness, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through transfer or payout. If instead delay undermines confidence, the node becomes a transmitter. Remember that time is the first constraint. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 182: feedback test for deposit insurers

Treat deposit insurers as a network component rather than an isolated balance-sheet line. Its system function is failure-loss allocation and depositor protection. Under loss revelation, change beliefs about asset value. Track coverage credibility and payout readiness and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether transfer or payout; contagion appears when delay undermines confidence. Because information becomes funding risk, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 183: second-round effects from deposit insurers

deposit insurers provide failure-loss allocation and depositor protection. After market-price gap, reduce collateral and capital values. Measure coverage credibility and payout readiness before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires transfer or payout. When delay undermines confidence, the shock becomes contagious. The core insight is that valuation becomes liquidity. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 184: deposit insurers under haircut increase

deposit insurers are modelled here as failure-loss allocation and depositor protection. Apply haircut increase: lower secured funding capacity. Observe coverage credibility and payout readiness. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is transfer or payout. The failure condition is that delay undermines confidence. The systems lesson is that collateral rules amplify price stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 185: how margin spike travels through deposit insurers

Start with the role of deposit insurers: failure-loss allocation and depositor protection. Shock the node by margin spike, which can create same-day cash demand. Measure coverage credibility and payout readiness, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through transfer or payout. If instead delay undermines confidence, the node becomes a transmitter. Remember that risk transfer becomes liquidity demand. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 186: feedback test for deposit insurers

Treat deposit insurers as a network component rather than an isolated balance-sheet line. Its system function is failure-loss allocation and depositor protection. Under wholesale closure, remove refinancing channels. Track coverage credibility and payout readiness and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether transfer or payout; contagion appears when delay undermines confidence. Because maturity transformation is exposed, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 187: second-round effects from deposit insurers

deposit insurers provide failure-loss allocation and depositor protection. After payment outage, delay settlement and create uncertainty. Measure coverage credibility and payout readiness before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires transfer or payout. When delay undermines confidence, the shock becomes contagious. The core insight is that operations become finance. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 188: deposit insurers under counterparty default

deposit insurers are modelled here as failure-loss allocation and depositor protection. Apply counterparty default: create direct loss and replacement need. Observe coverage credibility and payout readiness. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is transfer or payout. The failure condition is that delay undermines confidence. The systems lesson is that network claims transmit stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 189: how rating downgrade travels through deposit insurers

Start with the role of deposit insurers: failure-loss allocation and depositor protection. Shock the node by rating downgrade, which can raise spreads and collateral requirements. Measure coverage credibility and payout readiness, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through transfer or payout. If instead delay undermines confidence, the node becomes a transmitter. Remember that external classification changes behaviour. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 190: feedback test for deposit insurers

Treat deposit insurers as a network component rather than an isolated balance-sheet line. Its system function is failure-loss allocation and depositor protection. Under regime change, invalidate normal-period correlations. Track coverage credibility and payout readiness and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether transfer or payout; contagion appears when delay undermines confidence. Because historical averages understate nonlinear stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 191: second-round effects from resolution authorities

resolution authorities provide failure-management institutions. After rapid withdrawal, compress the funding clock. Measure critical-function continuity before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires transfer or other legal tools. When resolution execution creates uncertainty, the shock becomes contagious. The core insight is that time is the first constraint. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 192: resolution authorities under loss revelation

resolution authorities are modelled here as failure-management institutions. Apply loss revelation: change beliefs about asset value. Observe critical-function continuity. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is transfer or other legal tools. The failure condition is that resolution execution creates uncertainty. The systems lesson is that information becomes funding risk. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 193: how market-price gap travels through resolution authorities

Start with the role of resolution authorities: failure-management institutions. Shock the node by market-price gap, which can reduce collateral and capital values. Measure critical-function continuity, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through transfer or other legal tools. If instead resolution execution creates uncertainty, the node becomes a transmitter. Remember that valuation becomes liquidity. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 194: feedback test for resolution authorities

Treat resolution authorities as a network component rather than an isolated balance-sheet line. Its system function is failure-management institutions. Under haircut increase, lower secured funding capacity. Track critical-function continuity and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether transfer or other legal tools; contagion appears when resolution execution creates uncertainty. Because collateral rules amplify price stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 195: second-round effects from resolution authorities

resolution authorities provide failure-management institutions. After margin spike, create same-day cash demand. Measure critical-function continuity before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires transfer or other legal tools. When resolution execution creates uncertainty, the shock becomes contagious. The core insight is that risk transfer becomes liquidity demand. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 196: resolution authorities under wholesale closure

resolution authorities are modelled here as failure-management institutions. Apply wholesale closure: remove refinancing channels. Observe critical-function continuity. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is transfer or other legal tools. The failure condition is that resolution execution creates uncertainty. The systems lesson is that maturity transformation is exposed. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Propagation 197: how payment outage travels through resolution authorities

Start with the role of resolution authorities: failure-management institutions. Shock the node by payment outage, which can delay settlement and create uncertainty. Measure critical-function continuity, including both level and speed. A slow deterioration can be manageable while the same total change delivered quickly can breach a hard timing constraint.

Close the loop through transfer or other legal tools. If instead resolution execution creates uncertainty, the node becomes a transmitter. Remember that operations become finance. The model should name a falsifier: an observed state in which the assumed transmission edge does not appear.

Propagation 198: feedback test for resolution authorities

Treat resolution authorities as a network component rather than an isolated balance-sheet line. Its system function is failure-management institutions. Under counterparty default, create direct loss and replacement need. Track critical-function continuity and map who receives the resulting loss, liquidity need or information signal.

Resilience depends on whether transfer or other legal tools; contagion appears when resolution execution creates uncertainty. Because network claims transmit stress, the same protective action can be stabilising privately and destabilising systemically. Record both the institution-level and system-level sign of the feedback.

Propagation 199: second-round effects from resolution authorities

resolution authorities provide failure-management institutions. After rating downgrade, raise spreads and collateral requirements. Measure critical-function continuity before assuming the shock is absorbed. The question is whether the node has enough slack to act without exporting risk to another part of the system.

A stabilising path requires transfer or other legal tools. When resolution execution creates uncertainty, the shock becomes contagious. The core insight is that external classification changes behaviour. Record the next recipient of stress, the delay before it reacts, and the point at which a local response becomes a common market move.

Propagation 200: resolution authorities under regime change

resolution authorities are modelled here as failure-management institutions. Apply regime change: invalidate normal-period correlations. Observe critical-function continuity. The first question is whether the disturbance is idiosyncratic or shared across many institutions.

The stabilising response is transfer or other legal tools. The failure condition is that resolution execution creates uncertainty. The systems lesson is that historical averages understate nonlinear stress. A complete contagion test follows at least one second-round edge into market price, funding, collateral, capital, settlement or credit supply.

Authoritative reference shelf

For current U.S. financial-stability definitions of leverage, funding risk and fire-sale channels, see the Federal Reserve’s Types of Financial System Vulnerabilities and Risks. For the solvency-versus-liquidity evidence, see the New York Fed’s 2026 staff report Bank Failures: The Roles of Solvency and Liquidity and the Richmond Fed’s 2026 economic brief Bank Failures: Solvency and Liquidity.

For fire-sale and feedback modelling, see the Reserve Bank of Australia’s Contagion Modelling and Feedback Loops. For cross-sector liquidity and non-bank channels, see the IMF’s August 2026 Systemwide Stress Test at the IMF: Integrating Nonbank Financial Intermediary Risks. For recovery and resolution concepts, see the Federal Reserve’s Recovery and Resolution overview.

The proposition to remember

A bank run is a feedback system, not a single withdrawal event. Funding leaves; the institution responds; the response changes liquidity, asset prices, capital or beliefs; those changes alter the next funding decision. Contagion begins when that response changes the state of another institution or shared market.

This proposition avoids two bad simplifications. The first is that every bank run is irrational panic against a healthy institution. The second is that runs do not matter because weak fundamentals are often present. Both miss the path. Fundamentals shape vulnerability; funding speed shapes the deadline; asset sales shape realised loss; network structure shapes spillover.

For mathematics students, runs and contagion are therefore a study in nonlinear dynamics. Thresholds create regime changes. Shared assets create indirect networks. Margin creates state-dependent liquidity. Confidence changes transition probabilities. The most useful model is not the one that predicts one crisis perfectly; it is the one that exposes which feedback edge must break for the system to stabilise.