Reader question: When interest rates move, how does a bank estimate the change in its future net interest income instead of merely saying “rates went up, so margins should rise”?
The short answer is that a net-interest-income simulation is a timed cash-flow and repricing algorithm. It maps assets, liabilities and relevant off-balance-sheet positions onto future repricing dates, applies an interest-rate scenario, models how contractual and behavioural rates respond, projects interest income and expense over a chosen horizon, and compares the shocked result with a baseline.
What this page does — and does not do
This is a mathematics and computational-banking article about interest-rate risk in the banking book, or IRRBB. It is not a forecast of any bank’s earnings, not a recommendation about bank shares or deposits, and not a substitute for a bank’s binding supervisory rules. The Basel Framework defines IRRBB as risk to capital and earnings arising from adverse interest-rate movements; national implementation and a bank’s approved internal measurement system determine the exact regulatory treatment.
NII is a flow, not a market value
Net interest income is broadly the difference between interest income and interest expense, taking relevant hedges into account. That makes an NII simulation different from an economic-value-of-equity calculation. EVE asks how the present value of future banking-book cash flows changes. NII asks how interest earnings evolve over a shorter forward horizon, often with particular attention to the coming twelve months.
The same position can therefore look different through the two lenses. A long fixed-rate asset may have a large economic-value sensitivity even if its coupon income does not change immediately. A floating-rate loan may show limited price sensitivity but can reprice quickly and change NII.
The computational pipeline
A useful NII engine can be understood in six steps:
- Build the balance-sheet state. Capture principal, contractual rate, reference index, spread, next repricing date, maturity, currency and optionality for each relevant position.
- Construct the baseline path. Define the no-shock rate curves and assumptions about balances, maturities, customer behaviour and new business.
- Apply a shocked rate path. Shift the relevant risk-free or market curves according to a parallel or non-parallel scenario.
- Translate market rates into customer rates. Apply contractual reset rules, deposit betas, floors, caps, lags and behavioural assumptions.
- Project interest cash flows. Accrue income and expense through time using the shocked versus baseline rates and balances.
- Measure the difference. Calculate shocked NII minus baseline NII over the horizon and explain the contribution by product, currency, repricing bucket and risk driver.
The repricing ladder is the skeleton
The first essential data structure is a repricing ladder. A fixed-rate loan normally enters the ladder at maturity or another contractual repricing event. A floating-rate loan enters at its next reset. A term deposit has a contractual maturity. A non-maturity deposit has no contractual maturity, so its economic repricing behaviour must be modelled rather than read directly from a maturity date.
If assets reprice earlier than liabilities, an upward rate shock can initially increase NII because asset yields rise before funding costs fully catch up. If liabilities reprice faster, the opposite can occur. This is repricing or gap risk, but the real simulation must also handle basis risk and options.
A simple worked example
Consider an intentionally simplified one-year balance-sheet fragment:
- $100 million of floating-rate loans that reprice immediately with the reference rate;
- $80 million of deposits whose customer rate is assumed to pass through 50% of the same market-rate change;
- a parallel market-rate increase of 150 basis points;
- no balance growth, credit loss, fees, floors, hedges or timing lag in this first-pass illustration.
The loan yield rises by 1.50 percentage points, adding approximately:
$100m × 1.50% = $1.50m of annual interest income.
With a 50% deposit beta, the deposit rate rises by 0.75 percentage points, adding approximately:
$80m × 0.75% = $0.60m of annual interest expense.
The simplified NII change is therefore:
ΔNII ≈ +$1.50m − $0.60m = +$0.90m.
This is not a realistic bank forecast. It is a diagnostic example that isolates the transmission mechanism. Add a three-month deposit repricing lag, a loan-rate floor, customer withdrawals, changing balances, different reference curves or hedges, and the answer changes.
Deposit beta is not a constant of nature
A deposit beta is a compact description of how much a deposit rate changes relative to a market-rate change. If market rates increase by 100 bp and a deposit rate increases by 40 bp, the observed pass-through over that interval is 40%.
But the beta can depend on product type, customer segment, rate level, direction of the cycle, competition, digital switching, elapsed time and the bank’s liquidity needs. A single historical average can therefore be a weak forward assumption. The algorithm should distinguish instantaneous beta, cumulative beta and repricing lag rather than compress all three into one number.
This is why NII modelling connects directly to deposit-behaviour models.
Basis risk: when “rates” are not one rate
A parallel shock assumes a common movement, but banks often hold positions linked to different reference curves and tenors. A loan may reprice from one index while a hedge or liability references another. If those rates move by different amounts, the bank has basis risk.
A good NII engine therefore does not merely add 200 bp to every contract. It maps each position to its reference curve, applies the scenario to that curve, and preserves contractual spreads and reset conventions. Otherwise an apparently hedged position can look neutral even when the two sides actually reprice differently.
Non-maturity deposits turn a contractual problem into a behavioural one
Current accounts and many savings deposits can often be withdrawn without a contractual maturity date. Yet their balances may be operationally stable and their rates may reprice slowly. For IRRBB, banks therefore need behavioural assumptions about which balances are stable, how quickly they run off and how their administered rates respond to market rates.
This creates a weak link because the model is estimating a maturity that the contract does not contain. Basel IRRBB guidance explicitly recognises non-maturity deposits, loan prepayment and early term-deposit redemption as positions for which behavioural modelling can be important.
Static versus dynamic balance-sheet assumptions
Two simulations can apply the same rate shock and still produce different NII because they make different assumptions about future business.
Static balance sheet: the model broadly holds the balance sheet constant, often replacing maturing or repricing positions with comparable volumes under specified assumptions. This isolates rate sensitivity and improves comparability.
Dynamic balance sheet: the model allows balances, customer behaviour, product mix, pricing actions or management decisions to evolve with the scenario. This can be more realistic for planning but introduces more assumptions and more model risk.
Neither is universally “correct.” The page role must specify which question is being answered: pure sensitivity, regulatory disclosure, internal stress testing or business planning.
Current Basel shock calibration
On 16 July 2024, the Basel Committee finalised a recalibration of the prescribed IRRBB interest-rate shocks. The updated standard extended the calibration data through December 2023, moved from a 99th to a 99.9th percentile calibration, replaced global with currency-specific local shock factors and changed rounding from 50 bp to 25 bp. The revised calibration was to be implemented by 1 January 2026 and has been integrated into the consolidated Basel Framework.
This is an important update trigger. A simulation can be mathematically correct but regulatory-stale if it uses an obsolete shock table.
Inputs and outputs
Typical inputs include position balance, currency, product, fixed or floating status, coupon or administered rate, reference curve, contractual spread, next reset, maturity, payment frequency, floors and caps, behavioural maturity, prepayment assumptions, deposit beta and lag, hedge cash flows, baseline rate curve and shock scenario.
Useful outputs include baseline NII, shocked NII, ΔNII, contribution by product and currency, repricing-gap profile, deposit-pass-through contribution, basis-risk contribution, optionality contribution, hedge contribution and sensitivity to each major behavioural assumption.
Evidence polarity: what supports the simulation, and what argues against it?
Evidence for the result includes contracts that reconcile to source systems, observed reset behaviour matching contractual rules, historically stable deposit-segmentation behaviour, modelled prepayments that resemble realised outcomes, hedge cash flows that reconcile to valuation systems and scenario curves that match the approved shock definition.
Evidence against confidence includes systematic misses in deposit pass-through, unexplained customer migration, stale behavioural maturities, a growing difference between modelled and realised repricing, hedges whose reference curves do not match their mapped exposures, missing floors or caps, or large NII moves driven by assumptions that cannot be traced to data.
Failure modes and counterexamples
“Rates up means NII up.” False. If deposits or wholesale funding reprice faster than assets, an upward shock can reduce NII.
One beta for every deposit. A retail transaction account, savings account and rate-sensitive corporate deposit can behave very differently.
Ignoring lags. Two products can have the same long-run beta but very different first-year NII because one reprices immediately and the other gradually.
Assuming perfect hedge matching. Equal notionals do not eliminate risk when reset dates, tenors, curves, floors or behavioural maturities differ.
Confusing NII with EVE. A position can improve twelve-month earnings sensitivity while worsening long-horizon economic-value sensitivity.
Dynamic-model optimism. Allowing future pricing and customer actions can make a stress result look better if management responses are assumed too freely.
Diagnostics: how to test the weak links
- Reconcile opening balances and contractual rates to source systems before applying any scenario.
- Plot repricing cash flows by month and confirm that known fixed and floating products land in the correct buckets.
- Shock one curve at a time to isolate basis-risk contributions.
- Run deposit beta, lag and decay assumptions separately rather than changing them together.
- Compare predicted customer-rate changes with realised repricing after actual market moves.
- Run static and dynamic balance-sheet versions and explain the difference.
- Remove hedges and re-run the model; the sign and size of the change should make economic sense.
- Test floors, caps, zero or near-zero rates and very large shocks for discontinuities.
What would falsify confidence in the result?
Confidence should fall if repricing dates cannot be reconstructed from contracts; if a 0 bp scenario does not reproduce baseline NII; if a position linked to one curve reacts to an unrelated curve; if changing a deposit beta from 0% to 100% leaves deposit expense unchanged; if an expired hedge still affects the projection; or if the model repeatedly misses observed repricing after real rate changes without a documented explanation.
Alternatives answer different questions
NII simulation is one IRRBB lens. EVE measures the change in economic value across future cash flows. Duration and convexity provide useful approximations for simpler positions. Stress tests can layer liquidity, credit and customer-behaviour shocks onto interest rates. Funds-transfer-pricing systems allocate internal funding economics to business lines. None of these should be treated as a substitute for all the others.
How this connects to the surrounding mathematics
For the value perspective, see duration, convexity and interest-rate shocks. For behavioural liabilities, use deposit behaviour. Hedge construction connects to duration gaps, key-rate sensitivities and swaps. The internal economics of repricing also connect to funds transfer pricing.
Verification and update triggers
Store the scenario definition, curve date, balance-sheet snapshot, behavioural-model version, deposit beta and lag assumptions, optionality assumptions, hedge population, static/dynamic convention and forecast horizon. Re-run validation when the Basel IRRBB shock calibration changes, deposit behaviour shifts materially, new administered-rate products are launched, customer migration accelerates, hedging policy changes, or actual-versus-modelled NII differences breach a defined tolerance.
Primary and high-quality references
- Basel Committee on Banking Supervision, SRP31 — Interest rate risk in the banking book.
- Basel Committee, Interest rate risk in the banking book, final standard published in 2016.
- Basel Committee, Recalibration of shocks for interest rate risk in the banking book, 16 July 2024.
- Bank for International Settlements, IRRBB — Pillar 2 standardised framework: Executive Summary.
- BIS Quarterly Review, Interest rate risk management by EME banks, discussing repricing and deposit-rate sensitivity.
Educational boundary: This article explains rate-sensitivity mathematics. It does not forecast any bank’s earnings, prescribe a hedging strategy, or provide personalized financial or investment advice.