How does the banking system actually close its loop? The useful answer is longer than “banks take deposits and make loans.” Modern banking connects deposits, bank lending, money creation, payments, clearing and settlement, central-bank reserves, loan repayment, credit losses, liquidity, bank capital and new lending decisions. A loan can create a bank deposit; spending can move that deposit to another bank; interbank settlement can create a reserve-liquidity need; repayment can extinguish principal; default can reduce bank equity; and the realised outcome can feed back into pricing, underwriting and the next credit decision.

That sequence answers several common searches at once—how banking works, how banks create money, where loans come from, what happens when a loan is repaid, why banks need deposits and liquidity if lending creates deposits, how bank payments settle, and how credit losses affect capital—without flattening them into the same mechanism. The central distinction is between creating a claim, funding and settling the consequences of that claim, and closing the claim through repayment, refinancing, recovery or loss. Those stages live on different clocks and balance sheets.

In Singapore, a borrower may receive loan proceeds in a bank deposit and then send funds through ordinary retail payment rails such as FAST or PayNow; the customer experience can be nearly instantaneous while the banking system underneath still has to maintain accurate ledgers, meet payment and liquidity obligations, reconcile positions and remain within capital and risk constraints. The local infrastructure changes over time, but the mathematical architecture is durable: state → credit decision → balance-sheet change → payment → settlement → real-world use → cash-flow return → repayment or loss → capital/liquidity update → revised decision.

Boundary. This article teaches applied mathematics and systems reasoning. It is not lending advice, financial advice, investment advice, regulatory interpretation or banking-operating guidance. The institutional facts belong to central banks, regulators, payment-system operators and financial institutions; Bukit Timah Tutor’s role is to make the mathematical structure visible.

50-second router

For the whole-system map, start with Banking And Finance Closed Loop Systems | The Complete System.
For this article’s core idea, read The seven-stage banking loop.
For “do banks lend out deposits?”, read Loan creation is not a suitcase transfer.
For “why do banks still need deposits and funding?”, read Money creation is not liquidity creation at one bank.
For “what happens when a loan is repaid?”, read Principal repayment closes a balance-sheet loop.
For default, read When the loop returns as loss.
For equations and worked balance sheets, read Ledger laboratory.
For the existing specialist library, use Finance & Banking Algorithms | Applied Mathematics in Real Financial Systems.

The seven-stage banking loop

A compact banking loop can be written as seven stages: 1) capacity, 2) underwriting, 3) origination, 4) payment and settlement, 5) real-world use, 6) repayment or loss, 7) feedback. Capacity means that the bank has a viable balance sheet, funding plan, liquidity position, capital headroom, operational capability and risk appetite. Underwriting decides whether a borrower and transaction fit the bank’s criteria. Origination creates contractual claims and balance-sheet entries. Payment moves the newly available purchasing power. Real-world use determines whether the financed activity produces cash flow. Repayment or loss resolves the claim over time. Feedback changes future decisions.

Every stage has a different mathematical object. Capacity is a constrained optimisation problem. Underwriting is a probability and classification problem. Origination is double-entry accounting plus contractual cash-flow mathematics. Payment is a network and queueing problem. Real-world use is an uncertain cash-flow process. Repayment is a recurrence or amortisation problem. Default and recovery are stochastic loss processes. Feedback is a control problem with delay. Calling all of this simply “lending” hides the parts that actually fail.

The loop is also nested. A single loan has its own cycle, while the bank runs thousands or millions of loan cycles simultaneously. The payment system runs a much faster intraday cycle. Treasury runs funding and liquidity cycles. Capital planning runs monthly, quarterly and multi-year cycles. Monetary policy and the business cycle operate on still different horizons. Banking is therefore a hierarchy of coupled loops rather than one circular arrow.

Stage 1: capacity comes before credit

A bank can identify a willing borrower and still decide not to lend. The bank has to consider expected return, expected loss, capital consumption, liquidity implications, concentration, funding, maturity, operational capacity and strategic limits. In mathematics, these are constraints on the feasible set. A transaction outside the feasible set is not made even if its nominal interest rate looks attractive.

Capital is one constraint because unexpected loss can reduce equity. Liquidity is another because the deposit created at origination may be transferred elsewhere, producing settlement outflow. Funding is another because a bank whose deposit base or wholesale funding is unstable may not want to expand long-dated assets. Concentration is another because an individually acceptable loan can make a portfolio too dependent on one sector, geography or counterparty.

The constraint set itself moves. Retained earnings can expand capital. Losses can shrink it. Deposit inflows can improve funding but also create rate-sensitive liabilities. Market stress can raise wholesale funding cost. A downgrade can change collateral requirements. Regulation can alter definitions or required buffers. Capacity is therefore a state variable, not a permanent licence to lend.

Stage 2: underwriting converts uncertainty into a decision

Underwriting asks whether expected cash flow, collateral, borrower behaviour and contractual structure justify the risk. The mathematical temptation is to compress the answer into a score. Scores are useful, but a score is an intermediate representation, not the borrower. Probability of default, loss given default, exposure at default, affordability ratios, debt-service coverage and collateral values each describe a different dimension.

A useful expected-loss skeleton is EL = PD × LGD × EAD. If exposure is 100, probability of default is 2% and loss given default is 40%, the simple expected loss is 0.8. The calculation is not a complete pricing or provisioning framework, but it shows the multiplicative structure. Small errors in any input can matter. More importantly, PD and LGD are conditional on a future environment that can differ from the calibration sample.

Underwriting is already a feedback loop because models are built from past outcomes. Approve a certain borrower population today, observe repayment and default tomorrow, update model parameters, and use them for the next cohort. This creates selection effects: the bank observes rich outcomes for approved borrowers but sparse counterfactual outcomes for rejected applicants. A model can therefore learn the consequences of its own previous policy.

Stage 3: origination creates a loan claim and usually a matching deposit entry

The Bank of England’s “Money creation in the modern economy” explains a central mechanism clearly: when a commercial bank makes a loan, it commonly creates a matching deposit in the borrower’s account rather than taking a specific saver’s deposit and handing it over. In simplified double-entry form, the bank records +Loan asset and +Deposit liability. The borrower records +Deposit asset and +Loan liability. Both sides remain balanced.

This does not mean a bank can create limitless money at no cost. The borrower must want and qualify for credit. The bank must expect an adequate risk-adjusted return. Capital rules, liquidity rules, funding conditions, market discipline, internal limits and monetary conditions constrain expansion. A bank that originates a loan but cannot manage the payment and funding consequences has not solved the system problem.

It also does not mean every extension of credit has identical monetary effects. A new loan credited to a deposit differs from buying an existing asset from another bank, purchasing a government security from a non-bank, drawing on an existing credit line, securitising a loan, or lending in foreign currency through cross-border structures. Closed-loop analysis begins by writing the exact balance-sheet entries instead of applying slogans.

Loan creation is not a suitcase transfer from saver to borrower

The popular “warehouse of deposits” story imagines that deposits arrive first, are stored, and are then physically reallocated to borrowers. That can be a useful intuition for why stable funding matters, but it is not a complete description of modern deposit creation. A bank can create a deposit at the moment it books a loan. The key constraint is not whether one named depositor previously supplied the exact same monetary unit; it is whether the bank can sustain the resulting balance sheet and meet obligations that follow.

Why, then, do banks compete for deposits? Because deposits are a funding source and a payment liability. When the borrower spends the newly created deposit to someone at another bank, the originating bank can lose that deposit and must settle with the receiving bank. A stable deposit franchise can reduce reliance on more expensive or volatile wholesale funding. Deposit pricing, therefore, remains economically important even though loan origination can create deposits.

The apparent contradiction disappears once creation and migration are separated. Origination creates the customer deposit; payment can move the deposit claim to another bank; settlement moves reserve or settlement assets between banks; treasury manages the resulting funding position. One sentence about “banks create money” cannot replace those four stages.

Stage 4: spending converts a local bookkeeping event into a network event

Suppose Bank A lends Alicia 100 and credits her deposit 100. If Alicia pays Tricia, who also banks at Bank A, the bank can reduce Alicia’s deposit liability by 100 and increase Tricia’s deposit liability by 100. At the bank level, the total deposit liability can remain unchanged. The payment is economically important to the customers but may require no interbank reserve transfer.

Now suppose Tricia banks at Bank B. Bank A reduces Alicia’s deposit, Bank B increases Tricia’s deposit, and the two banks must settle the interbank obligation through the relevant payment infrastructure. In a simplified settlement, Bank A’s reserve or settlement balance falls and Bank B’s rises. The loan asset still sits on Bank A’s balance sheet. The deposit originally created at Bank A has migrated into a deposit at Bank B.

This is the hinge of the banking loop. Credit creation occurs on one balance sheet; spending redistributes deposits across balance sheets; settlement redistributes reserves or settlement assets; funding strategy responds to the new distribution. A bank can therefore be profitable on the loan and still face a liquidity problem if outflows are faster than its ability to fund or mobilise liquid assets.

Money creation is not liquidity creation at one bank

A newly created customer deposit is money for the customer, but it is a liability for the bank. If the customer sends it away, the bank has to meet the associated interbank settlement obligation. Creating a deposit does not automatically create a matching quantity of central-bank reserves for the originating bank. Central-bank reserves belong to a different layer of the monetary hierarchy.

The Federal Reserve’s 2025 reserve-balance explanation makes the distinction explicit in the US context: reserve balances are liabilities of the central bank and assets of depository institutions, and only the central bank can create them. The jurisdiction-specific operating framework varies, but the structural lesson is general. Commercial-bank deposit money and central-bank settlement money are linked but distinct.

This is why bank treasury matters. A bank forecasts payment outflows, deposit behaviour, collateral needs and funding maturities. It holds liquid assets, accesses markets and central-bank facilities under applicable rules, and manages its reserve or settlement position. The lending desk creates an earning asset; treasury ensures the institution can survive the cash consequences. Closed-loop banking requires both.

Stage 5: the loan leaves finance and enters the world

The most important part of a loan happens outside the bank ledger. A business borrower uses funds to buy equipment, inventory or labour. A household uses a mortgage to acquire a home. A student finances education. The financial claim is created immediately, but the activity that supports repayment unfolds over time. A bank can model expected cash flow; it cannot manufacture the borrower’s future revenue by accounting entry.

This stage is the “world-return” test. If the financed activity produces sufficient cash flow or the borrower otherwise earns sufficient income, contractual payments can return. If revenue disappoints, costs rise, employment is lost, assets fall in value or another shock occurs, the return path weakens. The credit model meets reality here.

A closed-loop article therefore separates financial creation from real creation. Credit can create purchasing power and claims; it does not itself guarantee more real output, productivity or income. Whether finance supports productive capacity, asset-price appreciation, consumption smoothing or loss depends on what happens after the funds are used.

Stage 6A: principal repayment closes a balance-sheet loop

When a borrower repays loan principal from a deposit at the same bank, the simplified balance sheet contracts. The bank reduces the borrower’s deposit liability and reduces the loan asset. The Bank of England’s money-creation article notes the symmetric point: repaying bank loans destroys deposit money just as new bank lending can create it. This is a system-level statement about bank-created deposits, not a claim that every payment anywhere destroys money.

Interest is different from principal. Principal reduces the outstanding loan claim. Interest is revenue to the bank before expenses, taxes, provisions and distributions. If the bank pays wages or dividends, the associated deposits can return to the non-bank sector. This is why “loan repayment destroys money” needs precision: the principal component and the income component have different accounting paths.

Prepayment changes timing. A borrower who repays early shortens the life of the asset, changing interest income, duration and reinvestment needs. Refinancing may close one loan while opening another, potentially at another institution. The individual contract closes, but the system can continue through a new claim.

Stage 6B: when the loop returns as loss

Default does not magically erase the bank’s liability structure. The bank recognises impairment, provisions and eventually write-offs according to applicable accounting and regulatory frameworks. Economically, the failed asset produces less value than expected. That shortfall reduces profit and can reduce equity. Recoveries from collateral, guarantees or later payments can offset part of the loss.

Loss given default is therefore a return-path variable. A 100 exposure with 60 recovery produces a 40 economic loss before other costs. If a portfolio experiences correlated defaults during a recession, losses can become nonlinear because collateral values may fall at the same time and recovery processes can become congested. The closed loop is not loan → default; it is loan → external conditions → default → recovery process → realised loss → capital/profit impact → new policy.

A bank with weak capital after losses may tighten underwriting, reduce limits, reprice loans or raise new equity. Those responses affect future borrowers and economic activity. Credit loss is thus both an endpoint for old loans and an input into new credit supply.

Stage 7: feedback changes the next borrower’s terms

Banks learn from outcomes through credit performance, profitability, collections, market conditions, stress tests, model validation and supervisory findings. If a cohort defaults more than expected, a bank may raise PD estimates, lower limits, strengthen affordability rules or increase price. If prepayment rises, it may alter product design or hedge assumptions. If deposit outflows accelerate, treasury may change transfer prices or liquidity buffers. Each change reshapes the next cycle.

The quality of this feedback depends on timing. A fast signal that is noisy can cause overreaction. A precise signal that arrives too late can be useless for prevention. Banking therefore combines leading indicators, contemporaneous controls and lagging outcomes. Model governance exists partly to decide when apparent change is real enough to justify recalibration.

Good feedback also travels across departments. If credit decisions ignore treasury cost, lending can be profitable only on a local metric. If treasury ignores borrower behaviour, deposit and prepayment assumptions can be wrong. If operations suppress exceptions without sending root-cause data back to product teams, failure repeats. A bank becomes more closed-loop as consequences return to the decision-maker who can alter the source.

The balance-sheet algebra of one loan

Use four state variables for a toy bank: loans L, reserves R, deposits D and equity E. Ignoring other assets and liabilities, a minimal identity is L + R = D + E. Real banks have many more balance-sheet categories, but the toy identity is enough to trace mechanics.

Start with L=800, R=200, D=900 and E=100. The bank originates a new loan of 100 and credits a deposit of 100. Then L=900, R=200, D=1,000 and E=100. Both sides rise from 1,000 to 1,100. No reserve transfer is required merely to make the internal bookkeeping entry.

If the borrower sends the 100 to a customer of another bank and Bank A settles 100 externally, Bank A can move to L=900, R=100, D=900 and E=100. Its balance sheet is again 1,000, but the composition has changed sharply: more loans, fewer reserves. The loan creation expanded the balance sheet; the external payment then replaced 100 of reserves with 100 of loans. This composition shift is why liquidity management matters.

If later the borrower earns income, receives 100 into Bank A, and repays 100 of principal, L falls to 800 and D falls by 100. The original principal claim closes. The path is not “deposit in → loan out → deposit back.” It is a sequence of balance-sheet transformations across institutions and time.

Principal, interest, fees and losses should never be mixed into one cash-flow bucket

A repayment schedule usually contains principal and interest. Principal is return of the amount lent; interest is compensation for time, risk, funding, capital and other economic factors. Fees may compensate for services or specific costs. Credit losses are negative outcomes on principal and sometimes accrued income. Each has a different accounting and risk meaning.

In an amortising loan, payment can be written as Payment = Interest component + Principal component. With periodic rate r and opening balance B, interest for a simple period is rB; principal is payment minus interest. The next balance is B’ = B(1+r) − Payment. Repeating the recurrence generates the amortisation path.

The existing BTT specialist article How Banks Calculate Loan Repayments: Amortisation, Compound Interest and Recurrence Relations owns the detailed recurrence mechanics. This article uses that recurrence only to connect repayment to the wider balance-sheet loop.

Why loan growth can look safest just before it becomes dangerous

Credit risk has a seasoning delay. A newly originated loan cannot be six months delinquent on day one. If a bank grows rapidly, the portfolio contains a large share of young loans that have not yet had time to reveal problems. Headline delinquency can fall simply because the denominator expanded with unseasoned accounts.

Vintage analysis repairs this by comparing cohorts at the same age. Month-12 delinquency for the 2026 cohort should be compared with month-12 delinquency for earlier cohorts, not with the total current portfolio. The model closes the time loop by aligning observation with exposure age.

This is a general systems lesson: a loop with long delay can accumulate error before feedback arrives. Growth can outrun measurement. The response is not to avoid growth but to include forward-looking indicators, underwriting drift checks, stress tests and conservative buffers while realised outcomes are still incomplete.

Interest rates connect borrower affordability, deposits, asset values and bank income

A change in interest rates can alter four parts of the loop simultaneously. It changes the price of new credit. It changes payments on floating-rate or refinancing borrowers. It changes deposit and wholesale funding costs. And it changes the market value of fixed-rate securities and sometimes hedges. The effects arrive at different speeds.

Suppose loan yields reprice immediately while deposit rates move slowly. Net interest income may initially rise. Months later deposit competition can increase funding cost. Borrowers may also face higher debt service, raising delinquency. Securities values may have fallen from the start. A one-variable story about “higher rates help banks” or “higher rates hurt banks” is therefore incomplete.

Closed-loop interest-rate modelling needs repricing ladders, behavioural assumptions, credit effects, market-value effects and funding responses. It also needs scenarios because customer behaviour changes when rates move beyond recent experience.

Funding is the bridge between asset creation and balance-sheet endurance

A bank funds its assets with a mixture of deposits, wholesale borrowing, secured funding, equity and other liabilities. The composition matters because each source has different maturity, price, stability, collateral and behavioural characteristics. A loan book with a ten-year horizon funded by overnight-sensitive liabilities creates a maturity mismatch even if the accounting identity balances perfectly.

The simplest funding loop is: assets determine funding need; funding markets and depositors determine price and availability; funding price enters loan pricing; loan pricing changes demand and portfolio growth; growth changes future funding need. Funds transfer pricing is one internal mechanism used to send those costs back to business lines.

A bank can therefore ration credit even when there are qualified borrowers. If marginal funding cost rises, the required loan price may become unattractive to borrowers. If wholesale markets close, growth can stop. If deposit betas rise, the economics of existing fixed-rate assets can weaken. Funding is not an afterthought to credit; it is part of the closed loop.

Capital is where old lending decisions constrain new lending decisions

Credit losses reduce earnings and can reduce capital. Capital ratios can then become tighter constraints on new business. Research from the BIS has documented links between bank capitalisation and loan terms and between equity and lending growth. The exact causal magnitude depends on institutions and periods, but the systems channel is clear: the condition of the balance sheet affects future credit supply.

A simplified capital ratio is Capital / Risk-weighted exposure. If capital stays at 100 while the denominator rises from 800 to 1,000, the ratio falls from 12.5% to 10%. If losses instead reduce capital from 100 to 80 while the denominator remains 800, the ratio falls to 10%. Growth and loss can therefore tighten the same ratio through different paths.

Management responses also differ. Growth-driven pressure can be addressed by slower expansion, portfolio changes or new capital. Loss-driven pressure may require earnings retention, capital raising, asset sales or more aggressive risk reduction. The mathematics must preserve the cause, not merely report the final ratio.

Liquidity is where payment timing constrains an otherwise viable bank

The bank can be profitable and solvent yet unable to settle a large outflow at the required moment. Liquidity therefore introduces a clock. Treasury forecasts cash inflows and outflows, holds liquid assets, monitors collateral and maintains contingency funding. Payment-system design determines how much liquidity is needed intraday and how often incoming settlement can be recycled.

A useful liquidity state equation is Available Liquidity(t+1) = Available Liquidity(t) + Settled Inflows + New Funding − Settled Outflows − Margin Calls − Other Uses. The state can change minute by minute. End-of-day data can conceal an intraday minimum that came close to failure.

The existing BTT article How Banks Stress-Test Liquidity owns the specialist stress mechanics. Here the liquidity equation exists to show how lending and payments re-enter the credit loop through a survival constraint.

Same-bank, different-bank and system-wide views

Alicia and Tricia make the hierarchy visible. Alicia borrows from Bank A. If she pays Tricia at Bank A, customer balances move within one liability ledger. If she pays Tricia at Bank B, two customer ledgers and two bank balance sheets change, plus interbank settlement. If Tricia then pays Kai Kai at Bank C, the deposit migrates again. The original loan remains at Bank A unless sold or transferred.

At the individual-bank level, deposits can leave. At the banking-system level, a transfer between commercial banks typically redistributes deposits rather than eliminating them. Principal repayment to a bank can reduce aggregate bank deposits under the simplified bank-money mechanism. Cash withdrawal can convert bank deposits into currency. Transactions with the central bank or government can have additional effects. The correct answer depends on the boundary of the accounting system.

This is why “where did the money go?” is not a one-ledger question. The same event can be an outflow for one bank, an inflow for another bank and no change in aggregate deposits. Systems mathematics must specify whether it is describing a customer, one bank, the banking sector, the central bank or the consolidated economy.

Singapore payment context: customer speed and bank settlement are different layers

The Association of Banks in Singapore currently explains PayNow as a service that lets customers of participating banks and major payment institutions send Singapore-dollar funds through FAST using identifiers such as mobile numbers and UENs. The user-facing convenience is an addressing and payment experience. Underneath it, participating institutions still manage their own ledgers, liquidity, controls and settlement obligations.

MAS’s current directory identifies FAST, Inter-bank GIRO, NETS EFTPOS, the Singapore Dollar Cheque Clearing System and the New MAS Electronic Payment and Book-Entry System among designated payment-system activities. Those names and operating details can evolve, so readers should use MAS’s current directory and the ABS PayNow page for current institutional facts.

The educational lesson does not require pretending every rail works identically. It requires separating the customer instruction from inter-institution obligation and final settlement. That separation makes it possible to reason correctly about why a loan-funded purchase can migrate deposits and create a liquidity requirement for the originating bank.

Alicia, Tricia and Kai Kai follow one loan for three years

Alicia owns the event timeline. At month 0 she receives a loan. On day 1 she spends the proceeds. Each month she makes payments. At month 18 she prepays part of the balance. At month 27 her income falls. At month 31 she misses a payment. At month 34 she cures the arrears. Alicia’s timeline reminds us that the credit state is path-dependent. “Current” today does not erase the fact that risk changed over time.

Tricia owns the ledgers. At origination she writes both sides of the bank and borrower entries. At external payment she moves the deposit and settlement positions. At each payment she separates principal from interest. If impairment is recognised, she records the loss path separately from cash settlement. Her discipline catches category errors before they become stories.

Kai Kai owns the failure test. At each stage he asks what would prevent the next stage from completing. Could the payment fail operationally? Could the bank lack settlement liquidity? Could Alicia lose income? Could collateral value fall? Could a model underestimate risk because similar borrowers were absent from the historical sample? His questions keep the loop attached to falsifiable conditions.

Twenty misconceptions corrected by the loop

“Banks can lend only money already deposited by savers.” — In modern commercial banking, loan origination can create a matching deposit; funding and liquidity still constrain the resulting balance sheet.
“If banks create deposits, deposits do not matter.” — Deposits are funding liabilities, can migrate between banks and influence liquidity and pricing.
“Creating a deposit creates central-bank reserves.” — Commercial-bank deposits and central-bank reserves are different liabilities issued by different institutions.
“A payment leaves the banking system.” — A transfer can simply move a deposit from one bank to another; the answer depends on the accounting boundary.
“Loan repayment is just cash income to the bank.” — Principal reduces the loan asset; interest is revenue. They are not the same flow.
“Default destroys the loan with no further consequence.” — Loss recognition, recovery, capital, provisioning and future underwriting all remain.
“A bank with positive equity cannot fail for liquidity reasons.” — A solvent bank can face obligations before it can mobilise cash.
“A bank with lots of cash must be solvent.” — Liquidity today does not prove that asset value exceeds liabilities after losses.
“High loan growth proves strong underwriting.” — Losses arrive with delay; young portfolios can look artificially clean.
“A credit score is the borrower.” — It is a model output conditional on data, definitions and calibration.
“One expected-loss number captures credit risk.” — Tail risk, correlation, timing, concentration and model error also matter.
“Interest-rate changes have one effect on banks.” — Assets, deposits, borrower behaviour and market values reprice differently.
“The fastest payment system always needs less liquidity.” — Faster gross settlement can reduce exposure time while increasing intraday liquidity demand.
“Netting is free efficiency.” — It reduces settlement amounts but introduces dependence on cycle completion and default rules.
“Capital is money sitting idle.” — Capital is a loss-absorbing funding concept; liquidity is a separate state.
“Profit immediately equals more lending.” — Distribution, risk limits, funding, demand and capital definitions intervene.
“Collateral removes credit risk.” — Collateral introduces valuation, haircut, legal and liquidity risk.
“A model that was accurate once stays accurate.” — Behaviour and regimes change; validation and recalibration close the model loop.
“The bank ledger proves the loan created value.” — The financed activity must return real cash flow or other economic value.
“One institution’s optimisation guarantees system stability.” — Common responses can amplify market and network stress.

Ledger laboratory: 30 worked transformations

1. New same-bank loan

Setup. Start Bank A: loans 800, reserves 200, deposits 900, equity 100. Originate 100 and credit Alicia’s deposit.

Closed-loop reading. Loans become 900 and deposits 1,000. Reserves and equity are unchanged at origination in this toy ledger. Total assets and liabilities-plus-equity both rise to 1,100. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

2. Same-bank purchase

Setup. Alicia pays Tricia 60 and both bank at Bank A.

Closed-loop reading. Alicia’s deposit falls 60 and Tricia’s rises 60. Total Bank A deposits do not change. The bank’s reserve position need not change merely because of this internal transfer. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

3. Cross-bank purchase

Setup. Alicia sends 60 from Bank A to Tricia at Bank B and the payment settles in central-bank money.

Closed-loop reading. Bank A’s deposits and reserves fall 60; Bank B’s deposits and reserves rise 60, ignoring fees and other flows. The banking system’s aggregate deposits can be unchanged by the transfer. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

4. Principal repayment

Setup. Alicia repays 20 principal from a deposit at Bank A.

Closed-loop reading. Bank A reduces the loan asset 20 and deposit liability 20. The simplified balance sheet contracts by 20. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

5. Interest payment

Setup. Alicia pays 3 interest from a deposit at Bank A.

Closed-loop reading. The deposit liability falls 3 and the bank recognises interest income, which ultimately affects retained earnings after expenses and taxes. It is not a reduction of loan principal. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

6. Full repayment

Setup. Outstanding principal is 40 and the borrower repays 40 from a same-bank deposit.

Closed-loop reading. Loan assets and deposits both fall 40. The contractual principal claim closes. Future interest on that principal no longer accrues. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

7. Partial prepayment

Setup. Outstanding principal is 100 and the borrower prepays 30.

Closed-loop reading. Principal falls to 70. Duration, future interest income and reinvestment needs change. The event can also alter prepayment-model calibration. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

8. Write-off

Setup. A 50 loan has no expected recovery and is written off after appropriate recognition.

Closed-loop reading. The asset is reduced. The economic loss has already or concurrently reduced income/equity through provisions or charge-offs depending on framework. The exact accounting path depends on applicable rules. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

9. Recovery

Setup. After a prior loss, 8 is recovered.

Closed-loop reading. Cash or deposits increase and recovery income or allowance effects are recognised under the applicable accounting framework. The recovery changes realised LGD estimates used in future modelling. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

10. Deposit inflow

Setup. Bank A receives 100 from another bank for a customer.

Closed-loop reading. Deposits rise 100 and settlement assets/reserves rise 100 in the toy example. The bank gains both a funding liability and liquid asset. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

11. Cash withdrawal

Setup. A depositor converts 20 of bank deposit into currency where the bank supplies cash.

Closed-loop reading. Deposits fall 20 and the bank’s cash asset falls 20. The customer changed the form of money held; the bank’s balance sheet contracts in this simplified example. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

12. Wholesale borrowing

Setup. Bank A borrows 100 overnight.

Closed-loop reading. Cash/reserves rise 100 and wholesale liabilities rise 100. Liquidity improves now but a maturity obligation is added. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

13. Wholesale maturity

Setup. The 100 overnight borrowing matures with no rollover.

Closed-loop reading. The bank must pay 100, reducing liquid assets unless replaced. A funding event becomes a liquidity event. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

14. Equity issuance

Setup. Investors contribute 50 of new equity cash.

Closed-loop reading. Liquid assets rise 50 and equity rises 50. Capital capacity can improve without creating a debt maturity. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

15. Dividend

Setup. The bank distributes 10 to shareholders.

Closed-loop reading. Cash or deposits fall and equity falls through the distribution. Retained capital is lower than it would have been without the dividend. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

16. Credit loss

Setup. A loan carrying amount is reduced by 15 due to realised or recognised loss.

Closed-loop reading. Assets and equity/income absorb the effect, subject to existing allowances. The loss tightens future capital headroom. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

17. Risk-weight increase

Setup. Capital stays 100; simplified risk-weighted exposure rises from 800 to 1,000.

Closed-loop reading. The ratio falls from 12.5% to 10%. No cash left the bank; a risk measurement changed the denominator. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

18. Reserve outflow

Setup. Bank A settles 25 to Bank B.

Closed-loop reading. Bank A’s reserve asset falls 25. If it was caused by a customer transfer, a matching deposit liability can also fall 25. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

19. Incoming settlement

Setup. Bank A receives 25.

Closed-loop reading. Reserve assets rise 25; the associated customer deposit or other obligation also rises depending on the payment. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

20. Queue release

Setup. A 30 incoming payment arrives and allows a previously queued 28 outgoing payment to settle.

Closed-loop reading. The same incoming liquidity supports later throughput. Peak intraday need can be far smaller than gross payment volume if liquidity recycles efficiently. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

21. Deposit-rate repricing

Setup. A bank raises a deposit rate while asset yields are fixed temporarily.

Closed-loop reading. Funding expense rises before asset income changes, compressing margin. Later asset repricing can offset the effect. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

22. Floating-loan repricing

Setup. Loan coupons reprice upward while deposits remain temporarily unchanged.

Closed-loop reading. Interest income rises initially, but borrower affordability can weaken and future expected losses can rise. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

23. Collateral haircut

Setup. An asset worth 100 is funded at a 10% haircut, then haircut rises to 25%.

Closed-loop reading. Funding capacity falls from 90 to 75. The bank needs 15 more collateral or cash to maintain the same borrowing. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

24. Margin call

Setup. A bank must post 12 additional collateral today.

Closed-loop reading. Available liquidity falls by 12 unless offset by incoming funds or collateral substitution. The economic hedge can be working while liquidity tightens. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

25. Loan sale

Setup. Bank A sells a 70 loan for cash at par.

Closed-loop reading. Loans fall 70 and cash/reserves rise 70. Credit exposure and funding composition change without necessarily changing total assets. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

26. Loan sale at discount

Setup. Bank A sells a loan carrying 70 for 63.

Closed-loop reading. Loans fall 70, cash rises 63 and a 7 loss reduces income/equity. Liquidity improves while capital weakens. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

27. Securitisation

Setup. A pool of loans is transferred into a structure and interests are sold.

Closed-loop reading. The accounting treatment depends on control and risk transfer. The systems point is that credit exposure, funding, liquidity and servicing can separate rather than disappear. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

28. Refinancing at another bank

Setup. Bank B lends a borrower 100, which is used to repay a 100 loan at Bank A.

Closed-loop reading. Bank B creates/advances the new claim; interbank payment settles to Bank A; Bank A’s old loan closes. The borrower’s debt continues but the creditor and funding network change. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

29. Refinancing at same bank

Setup. Bank A replaces an old 100 loan with a new 100 facility.

Closed-loop reading. The old contract can close while a new contract opens. Aggregate principal can be unchanged, but rate, maturity, collateral and risk parameters can change. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

30. Default plus recovery

Setup. A 100 exposure defaults and eventual recovery is 55.

Closed-loop reading. A simplified realised loss is 45 before costs. That outcome becomes data for LGD calibration and future pricing, closing the feedback loop. The point is to preserve which stock moved, why it moved, and which later decision receives the resulting information.

Credit-feedback atlas: 45 questions a serious banking model should answer

1. Borrower income shock

Question. How quickly does a fall in income appear in missed payments, account balances or line utilisation? Measure cash-flow volatility, delinquency migration and cure. The output must return to underwriting and early-warning thresholds; otherwise the institution is collecting information without closing the decision loop.

A rigorous version separates observation from inference. It records when the signal became visible, which state variable moved first, what lag exists before realised loss, and which competing explanation could produce the same pattern. The model should name a threshold that triggers review and a condition that would falsify the assumed causal link.

2. Sector recession

Question. How do correlated revenue losses change PD and recovery at the same time? Measure sector concentration, collateral correlation and default clustering. The output must return to limits, pricing and portfolio diversification; otherwise the institution is collecting information without closing the decision loop.

3. Property-price fall

Question. How does lower collateral value change LGD before and after default? Measure loan-to-value, sale discount and time to recovery. The output must return to origination LTV and capital planning; otherwise the institution is collecting information without closing the decision loop.

4. Rate rise

Question. Which borrowers reprice first and how does payment shock affect default? Measure repricing date, payment-to-income and arrears. The output must return to product mix and affordability stress; otherwise the institution is collecting information without closing the decision loop.

5. Rate fall

Question. Does refinancing or prepayment accelerate and shorten asset duration? Measure prepayment rate and refinance incentive. The output must return to pricing and hedging; otherwise the institution is collecting information without closing the decision loop.

6. Deposit competition

Question. How does a higher deposit beta feed into loan pricing? Measure funding cost and deposit retention. The output must return to transfer price and margin floor; otherwise the institution is collecting information without closing the decision loop.

7. Wholesale spread shock

Question. Which loan products remain economic after marginal funding cost rises? Measure spread, maturity and rollover risk. The output must return to origination mix; otherwise the institution is collecting information without closing the decision loop.

8. Capital drawdown

Question. What assets consume scarce capital most rapidly? Measure capital ratio and risk-weight density. The output must return to limits and asset allocation; otherwise the institution is collecting information without closing the decision loop.

9. Liquidity drain

Question. Which new loans create the largest expected settlement or funding need? Measure deposit migration, tenor and drawdown. The output must return to growth pace and liquidity pricing; otherwise the institution is collecting information without closing the decision loop.

10. Credit-line draw

Question. How do unused commitments become funded exposure during stress? Measure conversion factor and utilisation. The output must return to limit management and liquidity buffer; otherwise the institution is collecting information without closing the decision loop.

11. Mortgage prepayment

Question. How does faster principal return change income and duration? Measure hazard rate, seasoning and incentive. The output must return to hedge and reinvestment; otherwise the institution is collecting information without closing the decision loop.

12. Revolver cure

Question. Which delinquent accounts return to current and how long does it take? Measure roll rates, cure rate and balance. The output must return to collections strategy; otherwise the institution is collecting information without closing the decision loop.

13. Collections capacity

Question. When does case volume exceed human or automated resolution capacity? Measure queue arrival and service rate. The output must return to staffing and triage; otherwise the institution is collecting information without closing the decision loop.

14. Collateral delay

Question. How long between default, legal enforcement and cash recovery? Measure recovery timing and discount rate. The output must return to LGD and liquidity planning; otherwise the institution is collecting information without closing the decision loop.

15. Guarantee failure

Question. What if guarantor quality deteriorates with borrower quality? Measure wrong-way dependence. The output must return to credit enhancement value; otherwise the institution is collecting information without closing the decision loop.

16. FX borrower mismatch

Question. What happens when debt currency strengthens against borrower income currency? Measure FX sensitivity and debt service. The output must return to currency limits and hedging; otherwise the institution is collecting information without closing the decision loop.

17. Model drift

Question. When do observed defaults diverge from calibrated probabilities? Measure calibration slope, Brier score and cohort error. The output must return to recalibration trigger; otherwise the institution is collecting information without closing the decision loop.

18. Reject inference

Question. What information is missing because rejected applicants never became borrowers? Measure selection bias and missing labels. The output must return to model governance; otherwise the institution is collecting information without closing the decision loop.

19. Fraud at origination

Question. How does identity or income misrepresentation alter the observed credit distribution? Measure fraud flags and first-payment default. The output must return to verification controls; otherwise the institution is collecting information without closing the decision loop.

20. Economic recovery

Question. Which stressed borrowers cure as income improves? Measure cure probability and vintage. The output must return to provision release and pricing; otherwise the institution is collecting information without closing the decision loop.

21. Loan sale market

Question. Can the bank transfer exposure without taking a large discount? Measure bid depth and sale haircut. The output must return to liquidity contingency; otherwise the institution is collecting information without closing the decision loop.

22. Securitisation market

Question. Can funding and risk be redistributed and under what triggers? Measure advance rate, tranche attachment and investor demand. The output must return to origination economics; otherwise the institution is collecting information without closing the decision loop.

23. Concentration breach

Question. When does one borrower, group or sector dominate expected loss? Measure HHI and top-N exposure. The output must return to limits and syndication; otherwise the institution is collecting information without closing the decision loop.

24. Syndication

Question. How much exposure remains after distribution to other lenders? Measure hold level and allocation. The output must return to underwriting capacity; otherwise the institution is collecting information without closing the decision loop.

25. Covenant breach

Question. Does a warning signal arrive before payment default? Measure covenant headroom and waiver rate. The output must return to monitoring and restructuring; otherwise the institution is collecting information without closing the decision loop.

26. Restructuring

Question. Does payment relief improve recovery or only delay loss recognition? Measure NPV, redefault and cure. The output must return to workout policy; otherwise the institution is collecting information without closing the decision loop.

27. Forbearance

Question. Are modified terms masking persistent weakness? Measure post-modification performance. The output must return to classification and provision; otherwise the institution is collecting information without closing the decision loop.

28. Early repayment

Question. Does strong borrower quality remove the best assets from the portfolio first? Measure prepayment by score. The output must return to portfolio mix; otherwise the institution is collecting information without closing the decision loop.

29. Credit-score migration

Question. How fast do borrowers move between risk bands? Measure transition matrix. The output must return to limit and pricing; otherwise the institution is collecting information without closing the decision loop.

30. Vintage deterioration

Question. Do newer cohorts underperform older cohorts at the same age? Measure age-aligned delinquency. The output must return to underwriting change; otherwise the institution is collecting information without closing the decision loop.

31. Geographic shock

Question. Are borrowers exposed to the same local labour or property market? Measure regional concentration. The output must return to diversification; otherwise the institution is collecting information without closing the decision loop.

32. Climate event

Question. Does physical disruption affect income, collateral and insurance simultaneously? Measure location, downtime and loss severity. The output must return to scenario design; otherwise the institution is collecting information without closing the decision loop.

33. Supply-chain shock

Question. Can borrower failure propagate through customer or supplier links? Measure network exposure. The output must return to sector limits; otherwise the institution is collecting information without closing the decision loop.

34. Policy support expiry

Question. What happens when temporary relief ends? Measure payment jump and liquidity. The output must return to stress timing; otherwise the institution is collecting information without closing the decision loop.

35. Unemployment rise

Question. How does labour-market deterioration move household default? Measure income replacement and arrears. The output must return to PD scenario; otherwise the institution is collecting information without closing the decision loop.

36. Commodity shock

Question. How does price volatility affect producers and consumers differently? Measure cash-flow sensitivity. The output must return to sector scenarios; otherwise the institution is collecting information without closing the decision loop.

37. Digital-bank run

Question. How fast can deposit outflow overtake contingency funding mobilisation? Measure outflow velocity and concentration. The output must return to liquidity buffer; otherwise the institution is collecting information without closing the decision loop.

38. Operational payment outage

Question. Can borrowers or customers appear delinquent because transactions cannot process? Measure failed-payment queue. The output must return to exception handling; otherwise the institution is collecting information without closing the decision loop.

39. Data outage

Question. Can risk decisions continue safely with stale information? Measure data age and fallback coverage. The output must return to manual limits; otherwise the institution is collecting information without closing the decision loop.

40. Cyber fraud wave

Question. Can loss controls tighten without blocking legitimate liquidity? Measure fraud rate and false positives. The output must return to thresholds; otherwise the institution is collecting information without closing the decision loop.

41. Supervisory finding

Question. How does remediation change underwriting, capital or reporting? Measure finding severity and closure time. The output must return to governance; otherwise the institution is collecting information without closing the decision loop.

42. Accounting change

Question. How do new recognition rules change provision timing and ratios? Measure stage migration and allowance. The output must return to planning; otherwise the institution is collecting information without closing the decision loop.

43. Resolution concern

Question. Do counterparties withdraw funding before book insolvency? Measure spread and outflow. The output must return to contingency funding; otherwise the institution is collecting information without closing the decision loop.

44. Competitor repricing

Question. Does market competition force the bank below its risk-adjusted price floor? Measure approval, price and attrition. The output must return to strategy; otherwise the institution is collecting information without closing the decision loop.

45. AI underwriting adoption

Question. Does a new model improve discrimination without sacrificing calibration, fairness, explainability or stability? Measure AUC, calibration, override and drift. The output must return to model approval and monitoring; otherwise the institution is collecting information without closing the decision loop.

Thirty numerical mini-problems for students and analysts

1. Loan creation

Problem. A bank originates 250 and credits a deposit 250.

Answer. Assets and liabilities both rise 250 in the simplified bank ledger. The systems extension is to ask which next decision changes because of that result.

2. Cross-bank spend

Problem. Of the new 250 deposit, 180 is sent to another bank and settles externally.

Answer. The originating bank can lose 180 of deposits and 180 of reserves/settlement assets while keeping the 250 loan. The systems extension is to ask which next decision changes because of that result.

3. Same-bank spend

Problem. The remaining 70 is paid to another customer at the same bank.

Answer. Deposit ownership changes but aggregate bank deposits need not change. The systems extension is to ask which next decision changes because of that result.

4. Principal amortisation

Problem. A 1,000 balance has a period payment 110 and interest 50.

Answer. Principal reduction is 60; next balance is 940 before any other adjustments. The systems extension is to ask which next decision changes because of that result.

5. Interest-only period

Problem. A 1,000 balance has 5% period interest and payment exactly 50.

Answer. Principal does not fall in the simple model. The systems extension is to ask which next decision changes because of that result.

6. Negative amortisation

Problem. Interest is 60 but payment is 40.

Answer. Balance grows by 20 if unpaid interest is capitalised under the contract. The systems extension is to ask which next decision changes because of that result.

7. PD-LGD-EAD

Problem. PD 3%, LGD 45%, EAD 2,000.

Answer. Simple expected loss is 27. The systems extension is to ask which next decision changes because of that result.

8. Recovery

Problem. A defaulted 100 exposure returns 65 after costs.

Answer. Simple realised loss is 35. The systems extension is to ask which next decision changes because of that result.

9. Capital ratio

Problem. Capital 120, simplified RWA 1,000.

Answer. Ratio is 12%. The systems extension is to ask which next decision changes because of that result.

10. Capital loss

Problem. Capital falls 20 while RWA unchanged at 1,000.

Answer. Ratio falls to 10%. The systems extension is to ask which next decision changes because of that result.

11. RWA growth

Problem. Capital stays 120 while RWA rises to 1,200.

Answer. Ratio falls to 10%. The systems extension is to ask which next decision changes because of that result.

12. Deposit runoff

Problem. Deposits 2,000; gross outflow 300 and inflow 120.

Answer. Ending deposits are 1,820; net decline is 9% while gross outflow is 15%. The systems extension is to ask which next decision changes because of that result.

13. Reserve turnover

Problem. Opening reserves 50, settled inflows 200, settled outflows 220.

Answer. Closing reserves are 30, demonstrating that gross outflows can exceed opening liquidity through recycling. The systems extension is to ask which next decision changes because of that result.

14. Funding gap

Problem. Maturing liabilities 140, contractual inflows 80, immediately available liquidity 30.

Answer. The simple gap is 30 before other funding or asset sales. The systems extension is to ask which next decision changes because of that result.

15. Haircut

Problem. Collateral 200 with 20% haircut.

Answer. Lendable value is 160. The systems extension is to ask which next decision changes because of that result.

16. Haircut shock

Problem. Haircut rises to 35% on the same 200 collateral.

Answer. Lendable value falls to 130, a 30 reduction. The systems extension is to ask which next decision changes because of that result.

17. Deposit beta

Problem. Policy rate rises 1.5 percentage points; deposit rate rises 0.6.

Answer. Simple beta for that move is 0.4. The systems extension is to ask which next decision changes because of that result.

18. Spread

Problem. Loan yield 6%, marginal funding 3.5%, ignoring all other costs.

Answer. Raw spread is 2.5 percentage points; it is not risk-adjusted profit. The systems extension is to ask which next decision changes because of that result.

19. Loss-adjusted spread

Problem. Raw annual spread income 25 on exposure 1,000; expected credit loss 8.

Answer. Before other costs and capital charges, 17 remains. The systems extension is to ask which next decision changes because of that result.

20. Vintage default

Problem. Cohort A has 20 defaults among 1,000 by month 12; Cohort B has 35 among 1,000.

Answer. Simple month-12 default rates are 2% and 3.5%; B is 1.5 percentage points worse. The systems extension is to ask which next decision changes because of that result.

21. Roll rate

Problem. 200 accounts are 30-days past due and 50 become 60-days past due next month.

Answer. The simple forward roll rate is 25%. The systems extension is to ask which next decision changes because of that result.

22. Cure rate

Problem. Of 80 delinquent accounts, 32 return current.

Answer. Simple cure rate is 40%. The systems extension is to ask which next decision changes because of that result.

23. Credit-line utilisation

Problem. Limit 10,000; balance rises from 4,000 to 7,500.

Answer. Utilisation rises from 40% to 75%, a stress signal in some contexts. The systems extension is to ask which next decision changes because of that result.

24. Concentration

Problem. Largest borrower exposure 80 in portfolio 1,000.

Answer. Single-name concentration is 8% of portfolio exposure. The systems extension is to ask which next decision changes because of that result.

25. Prepayment

Problem. Opening mortgage pool 1,000; 100 voluntarily prepays during period, ignoring scheduled principal.

Answer. Simple period prepayment share is 10%. The systems extension is to ask which next decision changes because of that result.

26. Queue instability

Problem. Payment exceptions arrive 1,200/day; capacity resolves 1,000/day.

Answer. Backlog grows by 200/day without other changes. The systems extension is to ask which next decision changes because of that result.

27. Refinancing

Problem. Old loan 300 closes and new loan 300 opens at another bank.

Answer. Borrower principal is unchanged at the instant of refinance, but creditor, funding and risk ownership change. The systems extension is to ask which next decision changes because of that result.

28. Retained earnings

Problem. Profit 40, dividends 15.

Answer. Retained earnings add 25 to equity before other changes. The systems extension is to ask which next decision changes because of that result.

29. Leverage

Problem. Assets 1,000 and equity 50.

Answer. Simple assets-to-equity leverage is 20 times; a 5% asset loss would consume the starting equity if liabilities stay fixed. The systems extension is to ask which next decision changes because of that result.

30. World return

Problem. A financed project produces 120 operating cash flow before debt service on annual debt service 90.

Answer. Simple debt-service coverage is 1.33x before taxes, working-capital and definition adjustments. The systems extension is to ask which next decision changes because of that result.

How to build a bank-credit closed-loop model without fooling yourself

Begin with a precise boundary. Are you modelling one borrower, one bank, the banking sector, or the whole monetary system? Many apparent contradictions are boundary errors. A deposit transfer can be an outflow for one bank and a zero-sum redistribution for the sector. A principal repayment can reduce bank-created deposits at the sector level while interest income circulates differently. State the boundary before writing equations.

Next define stocks and flows. Loans outstanding, deposits, reserves, capital and collateral are stocks. Originations, repayments, withdrawals, settlements, losses and recoveries are flows. Then define timing. A daily payment model cannot be merged casually with a quarterly capital model. If two variables live on different clocks, write an aggregation or transition rule.

Then define feedback. Which observed outcome can actually change a future decision? A PD estimate matters only if pricing, approval, limits, provisions or monitoring react to it. A liquidity forecast matters only if treasury can raise funds, mobilise collateral, change payment sequencing or alter asset growth. Metrics without action channels are dashboards, not control systems.

Finally define falsifiers. What observed default rate would make the calibration unacceptable? What runoff speed would invalidate the deposit assumption? What settlement delay would breach the operating tolerance? What model drift triggers a challenger review? The closed loop is complete only when the model itself can be corrected.

Authoritative references and further reading

For the mechanics of commercial-bank money creation, see the Bank of England’s Money creation in the modern economy. For the distinction among currency, bank deposits and central-bank reserves, see Money in the modern economy: an introduction. For a current US explanation of reserve balances and their payment/liquidity role, see the Federal Reserve’s Interest on Reserve Balances FAQs.

For evidence on the connection between bank balance sheets, capital constraints and lending terms, see BIS research including How do credit ratings affect bank lending under capital constraints? and Why bank capital matters for monetary policy. For payment and settlement infrastructure, use the BIS–IOSCO Principles for Financial Market Infrastructures and the World Bank Payment Systems overview.

For Singapore, use the MAS designated payment-system directory and ABS PayNow for current institutional information. These references anchor domain facts; the equations and systems maps in this article remain educational abstractions.

Specialist Bukit Timah Tutor routes

The proposition to keep

A bank loan is not complete when it is approved or booked. The loop closes only when the claim survives payment, settlement, the borrower’s real-world use of funds, repayment or recovery, and the return of those outcomes into the bank’s capital, liquidity, pricing and next credit decision.

That proposition resolves several false arguments. Lending can create deposits and banks can still need stable funding. Principal repayment can reduce bank-created money and interest can still be bank income. A solvent institution can still be illiquid. A profitable loan can still weaken a bank if it consumes too much scarce capital or liquidity. A model can be statistically sophisticated and still fail if its feedback arrives too late.

For readers learning mathematics, banking is therefore not merely “finance with percentages.” It is an unusually rich closed-loop system in which accounting identities, recurrence relations, probability, statistics, networks, queues, optimisation and control theory all meet. The discipline is to trace the whole return path, preserve the boundary of each equation, and never let a local success metric masquerade as a system result.

Research workbook: 55 closed-loop investigations

Investigation 1: mortgage origination under a 200-basis-point rate shock

Treat mortgage origination as a closed-loop experiment. Its structural features are approval standards, collateral value and long maturity. Apply a 200-basis-point rate shock and reprice borrower cash flow and bank funding separately. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

The feedback evidence to collect is month-12 arrears and prepayment. The action channel is mortgage pricing and LTV policy. A complete answer states the lag between disturbance and observation, the threshold for intervention, the cost of a false alarm, the cost of a missed deterioration, and a competing hypothesis that could explain the same data. This converts a scenario from narrative stress into a falsifiable system model.

Investigation 2: mortgage origination under a 10% income decline

Treat mortgage origination as a closed-loop experiment. Its structural features are approval standards, collateral value and long maturity. Apply a 10% income decline and re-estimate affordability before changing collateral assumptions. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 3: mortgage origination under a 15% collateral-value fall

Treat mortgage origination as a closed-loop experiment. Its structural features are approval standards, collateral value and long maturity. Apply a 15% collateral-value fall and update recovery and secured-funding channels. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 4: mortgage origination under a two-week payment outage

Treat mortgage origination as a closed-loop experiment. Its structural features are approval standards, collateral value and long maturity. Apply a two-week payment outage and separate genuine arrears from operational failure. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 5: mortgage origination under a deposit-funding cost jump

Treat mortgage origination as a closed-loop experiment. Its structural features are approval standards, collateral value and long maturity. Apply a deposit-funding cost jump and send the cost through transfer pricing before judging product margin. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 6: mortgage origination under a recession scenario

Treat mortgage origination as a closed-loop experiment. Its structural features are approval standards, collateral value and long maturity. Apply a recession scenario and allow PD, LGD and utilisation to move together. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 7: mortgage origination under a rapid-refinancing wave

Treat mortgage origination as a closed-loop experiment. Its structural features are approval standards, collateral value and long maturity. Apply a rapid-refinancing wave and model prepayment as selection, not random attrition. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 8: mortgage origination under a model recalibration

Treat mortgage origination as a closed-loop experiment. Its structural features are approval standards, collateral value and long maturity. Apply a model recalibration and measure both discrimination and calibration before changing approval. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 9: mortgage origination under a capital-buffer squeeze

Treat mortgage origination as a closed-loop experiment. Its structural features are approval standards, collateral value and long maturity. Apply a capital-buffer squeeze and identify whether numerator rebuilding or denominator reduction drives response. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 10: mortgage origination under a liquidity freeze

Treat mortgage origination as a closed-loop experiment. Its structural features are approval standards, collateral value and long maturity. Apply a liquidity freeze and model funding maturity and settlement timing rather than annual averages. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 11: SME working-capital lending under a 200-basis-point rate shock

Treat SME working-capital lending as a closed-loop experiment. Its structural features are seasonal cash flow and short operating cycles. Apply a 200-basis-point rate shock and reprice borrower cash flow and bank funding separately. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

The feedback evidence to collect is utilisation, revenue and covenant movement. The action channel is limit renewal and pricing. A complete answer states the lag between disturbance and observation, the threshold for intervention, the cost of a false alarm, the cost of a missed deterioration, and a competing hypothesis that could explain the same data. This converts a scenario from narrative stress into a falsifiable system model.

Investigation 12: SME working-capital lending under a 10% income decline

Treat SME working-capital lending as a closed-loop experiment. Its structural features are seasonal cash flow and short operating cycles. Apply a 10% income decline and re-estimate affordability before changing collateral assumptions. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 13: SME working-capital lending under a 15% collateral-value fall

Treat SME working-capital lending as a closed-loop experiment. Its structural features are seasonal cash flow and short operating cycles. Apply a 15% collateral-value fall and update recovery and secured-funding channels. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 14: SME working-capital lending under a two-week payment outage

Treat SME working-capital lending as a closed-loop experiment. Its structural features are seasonal cash flow and short operating cycles. Apply a two-week payment outage and separate genuine arrears from operational failure. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 15: SME working-capital lending under a deposit-funding cost jump

Treat SME working-capital lending as a closed-loop experiment. Its structural features are seasonal cash flow and short operating cycles. Apply a deposit-funding cost jump and send the cost through transfer pricing before judging product margin. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 16: SME working-capital lending under a recession scenario

Treat SME working-capital lending as a closed-loop experiment. Its structural features are seasonal cash flow and short operating cycles. Apply a recession scenario and allow PD, LGD and utilisation to move together. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 17: SME working-capital lending under a rapid-refinancing wave

Treat SME working-capital lending as a closed-loop experiment. Its structural features are seasonal cash flow and short operating cycles. Apply a rapid-refinancing wave and model prepayment as selection, not random attrition. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 18: SME working-capital lending under a model recalibration

Treat SME working-capital lending as a closed-loop experiment. Its structural features are seasonal cash flow and short operating cycles. Apply a model recalibration and measure both discrimination and calibration before changing approval. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 19: SME working-capital lending under a capital-buffer squeeze

Treat SME working-capital lending as a closed-loop experiment. Its structural features are seasonal cash flow and short operating cycles. Apply a capital-buffer squeeze and identify whether numerator rebuilding or denominator reduction drives response. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 20: SME working-capital lending under a liquidity freeze

Treat SME working-capital lending as a closed-loop experiment. Its structural features are seasonal cash flow and short operating cycles. Apply a liquidity freeze and model funding maturity and settlement timing rather than annual averages. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 21: corporate term lending under a 200-basis-point rate shock

Treat corporate term lending as a closed-loop experiment. Its structural features are cash-flow coverage and concentration. Apply a 200-basis-point rate shock and reprice borrower cash flow and bank funding separately. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

The feedback evidence to collect is rating migration and covenant headroom. The action channel is hold level and syndication. A complete answer states the lag between disturbance and observation, the threshold for intervention, the cost of a false alarm, the cost of a missed deterioration, and a competing hypothesis that could explain the same data. This converts a scenario from narrative stress into a falsifiable system model.

Investigation 22: corporate term lending under a 10% income decline

Treat corporate term lending as a closed-loop experiment. Its structural features are cash-flow coverage and concentration. Apply a 10% income decline and re-estimate affordability before changing collateral assumptions. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 23: corporate term lending under a 15% collateral-value fall

Treat corporate term lending as a closed-loop experiment. Its structural features are cash-flow coverage and concentration. Apply a 15% collateral-value fall and update recovery and secured-funding channels. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 24: corporate term lending under a two-week payment outage

Treat corporate term lending as a closed-loop experiment. Its structural features are cash-flow coverage and concentration. Apply a two-week payment outage and separate genuine arrears from operational failure. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 25: corporate term lending under a deposit-funding cost jump

Treat corporate term lending as a closed-loop experiment. Its structural features are cash-flow coverage and concentration. Apply a deposit-funding cost jump and send the cost through transfer pricing before judging product margin. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 26: corporate term lending under a recession scenario

Treat corporate term lending as a closed-loop experiment. Its structural features are cash-flow coverage and concentration. Apply a recession scenario and allow PD, LGD and utilisation to move together. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 27: corporate term lending under a rapid-refinancing wave

Treat corporate term lending as a closed-loop experiment. Its structural features are cash-flow coverage and concentration. Apply a rapid-refinancing wave and model prepayment as selection, not random attrition. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 28: corporate term lending under a model recalibration

Treat corporate term lending as a closed-loop experiment. Its structural features are cash-flow coverage and concentration. Apply a model recalibration and measure both discrimination and calibration before changing approval. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 29: corporate term lending under a capital-buffer squeeze

Treat corporate term lending as a closed-loop experiment. Its structural features are cash-flow coverage and concentration. Apply a capital-buffer squeeze and identify whether numerator rebuilding or denominator reduction drives response. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 30: corporate term lending under a liquidity freeze

Treat corporate term lending as a closed-loop experiment. Its structural features are cash-flow coverage and concentration. Apply a liquidity freeze and model funding maturity and settlement timing rather than annual averages. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 31: credit cards under a 200-basis-point rate shock

Treat credit cards as a closed-loop experiment. Its structural features are revolving utilisation and behavioural scoring. Apply a 200-basis-point rate shock and reprice borrower cash flow and bank funding separately. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

The feedback evidence to collect is payment rate, delinquency and cure. The action channel is line assignment and pricing. A complete answer states the lag between disturbance and observation, the threshold for intervention, the cost of a false alarm, the cost of a missed deterioration, and a competing hypothesis that could explain the same data. This converts a scenario from narrative stress into a falsifiable system model.

Investigation 32: credit cards under a 10% income decline

Treat credit cards as a closed-loop experiment. Its structural features are revolving utilisation and behavioural scoring. Apply a 10% income decline and re-estimate affordability before changing collateral assumptions. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 33: credit cards under a 15% collateral-value fall

Treat credit cards as a closed-loop experiment. Its structural features are revolving utilisation and behavioural scoring. Apply a 15% collateral-value fall and update recovery and secured-funding channels. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 34: credit cards under a two-week payment outage

Treat credit cards as a closed-loop experiment. Its structural features are revolving utilisation and behavioural scoring. Apply a two-week payment outage and separate genuine arrears from operational failure. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 35: credit cards under a deposit-funding cost jump

Treat credit cards as a closed-loop experiment. Its structural features are revolving utilisation and behavioural scoring. Apply a deposit-funding cost jump and send the cost through transfer pricing before judging product margin. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 36: credit cards under a recession scenario

Treat credit cards as a closed-loop experiment. Its structural features are revolving utilisation and behavioural scoring. Apply a recession scenario and allow PD, LGD and utilisation to move together. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 37: credit cards under a rapid-refinancing wave

Treat credit cards as a closed-loop experiment. Its structural features are revolving utilisation and behavioural scoring. Apply a rapid-refinancing wave and model prepayment as selection, not random attrition. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 38: credit cards under a model recalibration

Treat credit cards as a closed-loop experiment. Its structural features are revolving utilisation and behavioural scoring. Apply a model recalibration and measure both discrimination and calibration before changing approval. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 39: credit cards under a capital-buffer squeeze

Treat credit cards as a closed-loop experiment. Its structural features are revolving utilisation and behavioural scoring. Apply a capital-buffer squeeze and identify whether numerator rebuilding or denominator reduction drives response. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 40: credit cards under a liquidity freeze

Treat credit cards as a closed-loop experiment. Its structural features are revolving utilisation and behavioural scoring. Apply a liquidity freeze and model funding maturity and settlement timing rather than annual averages. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 41: overdrafts under a 200-basis-point rate shock

Treat overdrafts as a closed-loop experiment. Its structural features are short-notice liquidity demand. Apply a 200-basis-point rate shock and reprice borrower cash flow and bank funding separately. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

The feedback evidence to collect is drawdown and account turnover. The action channel is limits and fees. A complete answer states the lag between disturbance and observation, the threshold for intervention, the cost of a false alarm, the cost of a missed deterioration, and a competing hypothesis that could explain the same data. This converts a scenario from narrative stress into a falsifiable system model.

Investigation 42: overdrafts under a 10% income decline

Treat overdrafts as a closed-loop experiment. Its structural features are short-notice liquidity demand. Apply a 10% income decline and re-estimate affordability before changing collateral assumptions. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 43: overdrafts under a 15% collateral-value fall

Treat overdrafts as a closed-loop experiment. Its structural features are short-notice liquidity demand. Apply a 15% collateral-value fall and update recovery and secured-funding channels. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 44: overdrafts under a two-week payment outage

Treat overdrafts as a closed-loop experiment. Its structural features are short-notice liquidity demand. Apply a two-week payment outage and separate genuine arrears from operational failure. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 45: overdrafts under a deposit-funding cost jump

Treat overdrafts as a closed-loop experiment. Its structural features are short-notice liquidity demand. Apply a deposit-funding cost jump and send the cost through transfer pricing before judging product margin. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 46: overdrafts under a recession scenario

Treat overdrafts as a closed-loop experiment. Its structural features are short-notice liquidity demand. Apply a recession scenario and allow PD, LGD and utilisation to move together. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 47: overdrafts under a rapid-refinancing wave

Treat overdrafts as a closed-loop experiment. Its structural features are short-notice liquidity demand. Apply a rapid-refinancing wave and model prepayment as selection, not random attrition. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 48: overdrafts under a model recalibration

Treat overdrafts as a closed-loop experiment. Its structural features are short-notice liquidity demand. Apply a model recalibration and measure both discrimination and calibration before changing approval. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 49: overdrafts under a capital-buffer squeeze

Treat overdrafts as a closed-loop experiment. Its structural features are short-notice liquidity demand. Apply a capital-buffer squeeze and identify whether numerator rebuilding or denominator reduction drives response. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 50: overdrafts under a liquidity freeze

Treat overdrafts as a closed-loop experiment. Its structural features are short-notice liquidity demand. Apply a liquidity freeze and model funding maturity and settlement timing rather than annual averages. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 51: auto finance under a 200-basis-point rate shock

Treat auto finance as a closed-loop experiment. Its structural features are depreciating collateral and instalment cash flow. Apply a 200-basis-point rate shock and reprice borrower cash flow and bank funding separately. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

The feedback evidence to collect is delinquency and recovery proceeds. The action channel is advance rate. A complete answer states the lag between disturbance and observation, the threshold for intervention, the cost of a false alarm, the cost of a missed deterioration, and a competing hypothesis that could explain the same data. This converts a scenario from narrative stress into a falsifiable system model.

Investigation 52: auto finance under a 10% income decline

Treat auto finance as a closed-loop experiment. Its structural features are depreciating collateral and instalment cash flow. Apply a 10% income decline and re-estimate affordability before changing collateral assumptions. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 53: auto finance under a 15% collateral-value fall

Treat auto finance as a closed-loop experiment. Its structural features are depreciating collateral and instalment cash flow. Apply a 15% collateral-value fall and update recovery and secured-funding channels. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 54: auto finance under a two-week payment outage

Treat auto finance as a closed-loop experiment. Its structural features are depreciating collateral and instalment cash flow. Apply a two-week payment outage and separate genuine arrears from operational failure. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Investigation 55: auto finance under a deposit-funding cost jump

Treat auto finance as a closed-loop experiment. Its structural features are depreciating collateral and instalment cash flow. Apply a deposit-funding cost jump and send the cost through transfer pricing before judging product margin. Write the opening state, the disturbance, the contractual flows and the earliest observable signal. Do not change every parameter at once; preserve enough structure to identify which channel is driving the result.

Final integration test: can you follow one unit of credit all the way home?

Take one unit of newly approved credit and refuse to stop tracing it until every relevant state transition has an owner. At origination, identify the bank asset and customer liability. At deposit creation, identify the customer asset and bank liability. At spending, identify whose deposit falls and whose rises. At interbank transfer, identify the settlement asset. At real-world use, identify the productive, household or asset transaction that is supposed to generate value. At repayment, split principal from interest. At default, identify recovery and loss. At the bank, identify the effects on earnings, liquidity and capital. Finally, identify which underwriting or pricing rule changes because of the realised outcome.

This exercise is deceptively demanding because it exposes any missing layer. If the story jumps from loan approval directly to repayment, it skipped payments and the real economy. If it jumps from deposit creation directly to “the bank has money,” it skipped the liability nature of deposits and the settlement layer. If it jumps from default directly to “the money vanished,” it skipped provisions, recoveries and capital. If it ends at capital without showing the next decision, it has not closed the feedback loop.

The highest-quality banking model is therefore not the one with the most equations. It is the one in which every equation has a boundary, every flow has an origin and destination, every delay is explicit, every constraint has a breach condition, and every outcome has a route back to the decision-maker. That is what makes the banking loop a mathematical system rather than a collection of financial vocabulary.

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Banking And Finance Closed Loop Systems | How the Banking Loop Closes From Deposits and Loans to Payments, Repayment and Loss