Quick answer: many bank deposits have no contractual maturity, yet customers do not all withdraw them tomorrow and banks do not reprice every account one-for-one with market rates. Banks therefore model two different behaviours: price behaviour, often summarised with a deposit beta that measures how much deposit rates move when a benchmark rate changes; and balance behaviour, often represented with decay, retention or behavioural-maturity assumptions. These models feed interest-rate risk, liquidity risk and funds-transfer-pricing systems. The central danger is assuming that behaviour observed in one rate or confidence regime will remain stable in another.

A current account has no maturity date in the contract. That does not mean its economic life is one day—or ten years.

Why this belongs in mathematics

Deposit modelling combines regression, elasticity, survival and decay curves, segmentation, scenario analysis, behavioural optionality and state-dependent transition. It also provides an excellent case study in normalcy blindness: when deposit balances have been stable for years, their stability can begin to feel like a property of the account rather than an observed behaviour produced by incentives, trust, convenience, competition and market conditions.

Basel’s interest-rate-risk framework explicitly treats non-maturity deposits (NMDs) as behaviourally modelled positions and requires banks to document, monitor and regularly update the assumptions used for their balances and repricing. See Basel SRP31 on interest-rate risk in the banking book.

1. What is a non-maturity deposit?

A non-maturity deposit is a deposit without a fixed contractual maturity or repricing date in the usual sense. Examples include many current/checking accounts, savings accounts and money-market deposit accounts.

Contractually, a customer may be able to withdraw quickly. Behaviourally, a large pool of customers can leave substantial balances in place for long periods. The bank therefore faces a modelling problem:

How much of today’s balance is likely to remain, for how long, and at what interest rate?

2. Deposit beta measures rate pass-through

A deposit beta is a simplified measure of how strongly a deposit rate responds to a movement in a market or policy rate. One intuitive version is:

Deposit beta ≈ Δ deposit rate / Δ driver rate.

If the policy or driver rate rises by 100 basis points and the bank raises a particular deposit rate by 40 basis points, the period beta is approximately 0.40, or 40%.

The Federal Reserve’s February 2026 Commercial Bank Examination Manual uses exactly this intuition: a 40-basis-point product-rate increase for a 100-basis-point driver-rate move corresponds to a 40% beta. It also notes that betas should be supported by analysis of the historical relationship between deposit products and their driver rates.

See the current Federal Reserve Commercial Bank Examination Manual, section 3300.1.

3. A beta is not a permanent constant

Suppose Bank A historically raised savings rates only slowly when policy rates rose. A model estimates beta = 0.25. If competition intensifies, customers discover higher-yield alternatives and the bank must raise deposit rates much faster, the future beta may be 0.60 or 0.80.

Recent academic evidence reinforces this. A 2025 Journal of Financial Intermediation study found that deposit pass-through varies with the interest-rate environment, reducing the usefulness of a fixed historical beta as a permanent hedge assumption. See Variable deposit betas and bank exposure to interest rate risk.

The model should therefore ask not only “What was beta?” but “Under which rate regime, competitive environment and customer mix was that beta observed?”

4. Instantaneous beta versus cumulative beta

Deposit rates often adjust with a lag. Suppose the policy rate rises 100 basis points today. The bank raises deposit rates 15 bps this quarter, another 10 bps next quarter and another 10 bps later. The immediate beta is only 15%, but cumulative pass-through reaches 35%.

A model that looks only at same-quarter changes can therefore understate the eventual funding-cost response. Distributed-lag or dynamic regression models can estimate the path of pass-through rather than one contemporaneous coefficient.

5. Up-cycle and down-cycle behaviour may be asymmetric

Banks may be slow to raise deposit rates early in a tightening cycle, then accelerate once customers become rate-sensitive. When market rates fall, deposit rates may also decline at a different speed because floors, customer relationships and competitive pressures are asymmetric.

That means one linear beta estimated across rising and falling rate cycles can average away the very behaviour the risk model needs to see.

A useful challenger model estimates separate up-cycle and down-cycle pass-through, or lets beta vary with the level and direction of market rates.

6. Decay rates model balance runoff

Price behaviour is only half the problem. The bank also needs to estimate how deposit balances leave over time.

Let d be a simple annual decay rate for a deposit cohort. If B₀ is the starting balance, an elementary exponential-decay model is:

B_t = B₀(1 − d)^t.

If S$100 million of a deposit segment has a 20% annual decay assumption, the simplified surviving balance after one year is S$80 million, after two years S$64 million and after three years S$51.2 million.

This is a teaching model, not a recommendation. Real deposit decay is rarely a smooth constant exponential process. New deposits arrive, customer cohorts differ and stress can produce abrupt nonlinear runoff.

7. Behavioural maturity comes from the decay profile

If a stable portion of deposits is expected to persist, banks can assign behavioural cash-flow dates or replication portfolios to that core balance for interest-rate-risk and FTP purposes.

The Federal Reserve cautions that institutions should support NMD decay assumptions with their own profile and activities rather than relying blindly on industry or vendor averages. Customer type and geography can produce materially different behaviour.

See the Fed’s Interest-Rate Risk FAQs.

8. “Core deposit” is a modelled population, not a moral category

A bank may identify a proportion of deposits as relatively stable or “core” for modelling purposes. But a deposit does not become permanently stable because it received the label.

Useful segmentation dimensions include:

retail versus wholesale;
transactional versus non-transactional;
insured versus uninsured;
consumer versus corporate;
operational relationship versus rate-seeking balance;
digital-only versus relationship-based customer;
balance size;
customer tenure;
geography and market competition.

Basel specifically expects NMD assumptions to vary with depositor and account characteristics rather than treating the deposit base as homogeneous.

9. Deposit beta and decay interact

Suppose a bank keeps deposit rates low while market rates rise. That creates a low observed beta and protects near-term interest margin. But customers may respond by moving balances elsewhere, increasing decay.

Alternatively, the bank can raise deposit rates faster. Beta rises, funding costs increase, but balance runoff may slow.

The bank is therefore solving a joint behavioural problem:

Deposit pricing → customer response → balance retention → funding cost → liquidity and interest-rate risk.

A model that estimates beta and decay independently can miss this feedback.

10. The deposit model feeds several other bank algorithms

System	How deposit behaviour enters
Net interest income simulation	Deposit beta controls repricing cost
Economic value / IRRBB	Behavioural maturity and decay determine cash-flow timing
Liquidity stress testing	Runoff assumptions determine cash outflows
Funds transfer pricing	Stable balances receive term funding benefit based on behavioural value
Contingency funding	Concentration and speed assumptions affect required liquidity capacity

This is why a small error in deposit modelling can propagate across several reports. One optimistic “sticky deposit” assumption can simultaneously improve apparent liquidity, lower FTP costs and reduce measured interest-rate risk.

For the internal-pricing connection, see How Banks Use Funds Transfer Pricing Algorithms.

11. Digital withdrawal changes the speed limit

Traditional deposit models were often built from historical observations in which large withdrawals required more friction: phone calls, branch interactions, slower information flow or manual treasury processes. Mobile and online banking reduce that friction.

The Federal Reserve’s review of Silicon Valley Bank emphasised the extraordinary speed and scale of deposit outflows and identified the bank’s concentrated uninsured deposit base, weak liquidity-risk management and changing technology/social dynamics as important context. See the Federal Reserve review of Silicon Valley Bank.

The lesson for modelling is not “every future bank run will look like SVB.” It is that the historical distribution of withdrawal speed is not guaranteed to be stationary after the transaction technology changes.

12. A digital run is not merely a higher decay rate

Normal decay and stress runoff are different states. A 15% annualised normal decay curve cannot simply be multiplied until it resembles a one-day run. Stress withdrawal can be correlated, strategic and information-driven.

A bank therefore needs at least two behavioural regimes:

business-as-usual retention and repricing; and
stress runoff under loss of confidence, rate competition or market disruption.

The second regime belongs in liquidity stress testing rather than being disguised as a slightly faster version of the first.

13. Creative-work lens: from Mary Poppins to a smartphone screen

The bank-run scene in Mary Poppins is memorable because panic becomes physical: people gather, demand cash and transmit fear face to face. That creative image helps us understand coordination. But a modern run may have no queue outside the branch. The “queue” can be millions of digital instructions arriving through apps and corporate treasury portals.

The story is useful because it reveals the human mechanism; the modern model must then remove the old physical constraint. If the withdrawal channel changes, a historical decay curve built around branch-era friction can become a background assumption nobody remembers to question.

14. The algorithmic pipeline

Segment deposit accounts. Separate customer and product populations with genuinely different behaviour.
Choose driver rates. Policy rates, wholesale rates and competitor pricing may influence each product differently.
Estimate short-run and cumulative betas. Allow for lags and asymmetry.
Estimate balance retention and decay. Cohort, survival or time-series methods can be used.
Identify stable/core components cautiously.
Translate retained balances into behavioural cash-flow maturities.
Feed assumptions into NII and EVE models.
Feed stable-funding value into FTP.
Build separate stress-runoff assumptions for liquidity testing.
Test digital-channel and concentration effects.
Backtest rate pass-through and actual runoff.
Re-segment and recalibrate when customer behaviour changes.

15. Failure modes

Constant-beta assumption. A historical average is treated as valid at every rate level.
Symmetry assumption. Rising- and falling-rate cycles are forced into one coefficient.
Contractual-maturity literalism. All demand deposits are treated as overnight funding.
Behavioural overextension. Stable historical balances are assigned excessively long economic lives.
Beta/decay separation. The model ignores that lower deposit rates can cause higher runoff.
Population mixing. Insured retail accounts and concentrated corporate balances share one decay curve.
Normalcy contamination. Years of stable behaviour become an unquestioned belief that balances are inherently stable.
Digital-friction blindness. Historical withdrawal speed is reused after technology changes the execution channel.

16. Diagnostics and falsifiers

Does beta rise as market rates reach higher levels?
How much pass-through arrives with a one- or two-quarter lag?
Do balances with the lowest relative rates experience faster runoff?
Which customer segment has the shortest observed retention?
How different are insured retail and uninsured corporate decay profiles?
Does a behavioural-maturity assumption survive a high-rate competitive period?
How quickly could the top 20 depositors move funds through current digital channels?
What happens to EVE, NII and liquidity simultaneously if beta and decay both rise?

Suppose someone claims, “These deposits have been stable for ten years, so we can model them as ten-year funding.” A falsifier is a rate or confidence regime in which the same customer population rapidly reprices or withdraws. Historical persistence is evidence about behaviour; it is not a contractual guarantee.

17. Verification and update triggers

backtest beta by product and customer segment;
measure cumulative pass-through rather than only same-period response;
compare predicted and realised deposit decay;
track rate-gap effects on deposit growth;
re-estimate after major policy-rate cycles;
update segmentation after acquisitions, customer-mix changes or new digital channels;
stress the largest uninsured and concentrated balances separately;
challenge any assumption that improves FTP, liquidity and IRRBB simultaneously without new supporting evidence.

Connections across the finance-and-banking algorithms lane

Funds transfer pricing — behavioural maturity determines the internal funding value of deposits.
Liquidity stress testing — stress runoff is the severe-regime counterpart to normal decay.
Interest-rate risk — deposit beta and maturity assumptions can dominate EVE and NII.
Interbank network contagion — what can happen beyond the institution once liquidity stress propagates.

Research anchors

The deeper lesson

Deposit modelling is the mathematics of a contract that leaves behaviour open. Customers choose when to move money and banks choose how quickly to reprice it. Betas estimate the price response. Decay curves estimate the balance response. Stress scenarios ask when both relationships can break at once. A strong model therefore treats deposit stability as something that must keep earning its evidence—not as a permanent property inherited from the past.

Educational note: This article explains banking mathematics and public risk-management concepts. It is not financial advice, deposit advice, a prediction of any bank run or institution-specific regulatory guidance.

Small Group Tutorials

How Banks Model Deposit Behaviour: Deposit Betas, Non-Maturity Deposits, Decay Curves, Rate Pass-Through and Digital Run Risk