A bank often makes loans whose rates are fixed for several years while funding them with deposits that can reprice or leave much sooner. Interest-rate risk in the banking book, or IRRBB, arises when changes in rates affect the bank’s earnings or the economic value of these assets and liabilities. It includes differences in repricing dates, differences between reference rates and options exercised by customers.

This module uses two complementary views. Net interest income measures the effect on interest earnings over a defined period. Economic value of equity compares the present value of asset and liability cash flows over their remaining lives. A decision can improve one view while worsening the other, so neither should be interpreted in isolation.

You will build cash flows, apply rate shocks and explore deposit behaviour, prepayments, basis risk and hedges. Later examples connect the calculations to supervisory shock conventions, reporting and governance. Start with the overview, then change one balance-sheet feature at a time. The module identifies whether an input is a behavioural assumption, a simplified model choice or part of the cited PRA and Basel framework.

Continue your learning: Yield curves and bootstrapping · Treasury risk · Liquidity and funding risk

Look up a term as you work through the examples. Definitions explain the terminology; the source references and assumptions beside each lesson explain the scope of its calculation.

89 definitions

Absorbing state

An absorbing state is a model state that cannot be left once entered. Treating default as absorbing is a modelling choice that excludes subsequent cures from that transition model.

Accrual

Accrual allocates interest or other income and expense to the period in which it is earned or incurred. Accrued interest can make a settlement amount differ from a quoted clean bond price.

Accrued interest

Accrued interest is interest earned or owed since the last payment date but not yet paid. Its calculation depends on the contract’s day-count and payment conventions.

Actual, hypothetical and risk-theoretical P&L

P&L means profit and loss. Actual P&L follows the applicable realised desk calculation; hypothetical P&L revalues a specified static portfolio; risk-theoretical P&L uses the risk factors represented by the model. Their definitions and exclusions must be matched before comparing them.

ALCO

The Asset and Liability Committee considers balance-sheet risks and trade-offs such as funding, liquidity, earnings and economic value. Its precise authority and reporting responsibilities depend on the organisation’s governance.

Asset

An asset is a resource or contractual right with economic value. For a bank, examples include cash, securities and loans that customers are expected to repay.

Backtesting

Backtesting compares model outputs with subsequent or historical outcomes under a defined testing convention. A breach or exceedance occurs when the observed loss is beyond the relevant model threshold; count, size and data dependence all affect interpretation.

Basel, BCBS and IOSCO

The Basel Committee on Banking Supervision develops international prudential standards for banks. IOSCO is the International Organization of Securities Commissions. International standards require the relevant jurisdictional implementation before they can be treated as local rules.

Basis point

One basis point is one hundredth of a percentage point. A rise from 4.00% to 4.01% is a one-basis-point increase.

Basis risk

Basis risk arises when two related prices or rates do not move together as assumed. A hedge tied to one benchmark may therefore leave exposure to a different benchmark, location or contract specification.

Bond

A bond is a debt security under which an issuer promises specified payments to investors. Its value depends on the timing of those payments, discount rates and the risk of non-payment.

Calibration

Calibration selects model parameters to match chosen data, market prices or target risk properties. A calibrated model can still be inappropriate if its structure or the selected evidence does not suit the task.

Call and put

A call gives the holder the right to buy the underlying on the contract’s terms. A put gives the right to sell it. The holder’s exercise choice makes the payoff asymmetric.

Cash flow

A cash flow is a payment or receipt at a specified time. Its amount, date, currency and legal owner affect both valuation and liquidity.

Collateral

Collateral is cash or another eligible asset provided to secure an obligation. Its protection depends on value, legal enforceability, availability and the time required to realise it.

Concentration

Concentration means that a large share of exposure or funding depends on a small number of sources or common drivers. The Herfindahl–Hirschman Index, or HHI, sums squared shares to measure size concentration but does not by itself measure behavioural dependence.

Correlation

Correlation summarises a specified relationship between two variables. A linear correlation does not fully describe joint tail behaviour, and a prescribed regulatory correlation is a model parameter rather than a measured relationship for every portfolio.

Counterparty credit risk

Counterparty credit risk is the risk of loss when the other party to a financial contract fails to perform. For derivatives, exposure can change with market conditions and may be positive for either party at different times.

Coupon

A coupon is an interest payment on a bond or loan. The coupon rate determines the contractual payment; it is not necessarily the yield available to an investor at the current market price.

Credit spread

A credit spread is the additional yield or premium associated with credit exposure relative to a reference rate. It can reflect default risk, liquidity and other market effects, so it is not a direct default probability.

CS01

CS01 measures the value effect associated with a one-basis-point credit-spread move. A bond holder and a buyer of credit protection can have opposite signed CS01 values.

Currency codes

GBP denotes pounds sterling, USD denotes US dollars, EUR denotes euros and JPY denotes Japanese yen. Currency labels matter because values and thresholds must be converted consistently before they are compared or combined.

Curvature

Curvature describes the part of a value change that a first-order sensitivity does not capture. Its regulatory construction differs by framework: FRTB uses specified repricing shocks, whereas SIMM derives a curvature exposure from volatility-weighted vega and expiry scaling.

CVA

Credit valuation adjustment reduces a default-free value to reflect expected loss from counterparty default under the selected valuation framework. The value of CVA and the capital held against changes in CVA are different measures.

Deposit beta and lag

Deposit beta measures the proportion of a market-rate change passed into the customer deposit rate. Lag measures the delay before that repricing occurs; neither is a deposit withdrawal rate.

Discount factor

A discount factor is the multiplier that converts a future cash flow into present value. Its value depends on maturity and the discounting convention.

Discount rate

A discount rate is a rate used to value future cash flows in present terms. The appropriate rate depends on the valuation framework and the characteristics of the cash flow.

Distribution

A probability distribution assigns probabilities to possible values or outcomes. It describes a range of possibilities rather than one realised observation.

Drift and diffusion

Drift describes the predictable local direction of a stochastic process under a chosen probability measure. The diffusion term determines the magnitude of its continuous random fluctuations.

Duration

Duration summarises the timing of cash flows or their sensitivity to rates, depending on the definition. Macaulay duration is a present-value-weighted time, while modified duration estimates proportional price sensitivity to yield.

DV01

DV01 measures the value effect associated with a one-basis-point interest-rate move. Some systems report a signed price change and others report a positive loss magnitude, so the lesson’s sign convention must be checked.

Economic value of equity

Economic value of equity compares the present value of the relevant asset and liability cash flows under the chosen measurement convention. Delta EVE is the scenario change in that value and is not the same as a short-term earnings change.

Equity

Equity represents an ownership interest. On a bank balance sheet, equity is the residual interest in assets after liabilities; in a market-risk example, an equity position usually means shares in a company.

Expectation

Expectation is an average weighted by the probabilities in a model. Conditional expectation updates that average using specified information and considers only the outcomes consistent with it.

Expiry

Expiry is the time at which an option’s exercise right ends. A European option can be exercised only at expiry, while other exercise styles allow different choices.

Floating rate

A floating rate resets according to a benchmark or contractual rule. Repricing occurs when the rate used to calculate a payment is updated, which need not coincide with repayment of principal.

Forward contract

A forward contract fixes today the terms of a transaction to occur at a future date. The value of an existing forward changes as current market prices and financing conditions change.

Funding and rollover risk

Funding supports assets and payment obligations through deposits, borrowing and other sources. Rollover risk is the risk that maturing funding cannot be replaced at an acceptable cost or at all.

FX swap and forward points

An FX swap exchanges currencies now and reverses the exchange at a later date. Forward points express the difference between forward and spot exchange rates; basis and market conventions affect the all-in funding interpretation.

Gamma

Gamma measures how delta changes as the underlying changes. Convexity describes curvature more generally; bond convexity usually refers to the second-order relationship between price and yield.

Haircut

A haircut reduces the recognised value of collateral or an asset pool for a specified calculation. It accounts for the relevant risk or rule and is not necessarily the price discount obtained in an actual sale.

Hedge

A hedge is a position intended to offset part of another exposure. It can leave basis, timing, legal or non-linear risks and can introduce its own funding and counterparty demands.

Independence

Variables are independent when learning the value of one does not change the probability distribution of the other. This is stronger than having zero linear correlation.

Index decomposition

Index decomposition represents a position through exposures to its constituents when the relevant framework permits or requires it. Delta, vega and curvature can have different index treatments, so look-through should not be applied indiscriminately.

Initial margin

Initial margin is a buffer for potential adverse value movements during the period needed to close or replace positions after default. It is separate from variation margin and can create a funding requirement for the posting party.

Interest rate

An interest rate expresses the cost of borrowing or the return on lending over a stated period. Its meaning depends on the currency, term, compounding convention and credit or collateral conditions.

Interest-rate swap

An interest-rate swap exchanges interest payments calculated on a reference notional. A common swap exchanges fixed interest for floating interest, allowing the parties to change their exposure to future rates.

IRRBB and CSRBB

IRRBB is interest-rate risk in the banking book and concerns earnings and economic-value effects. CSRBB is credit-spread risk in the banking book and addresses relevant spread movements that are distinct from general interest-rate changes.

Liability

A liability is an obligation to transfer money or another resource. Customer deposits and a bank’s own borrowings are liabilities because the bank owes those amounts.

Liquidity and solvency

Liquidity concerns the ability to meet obligations when due. Solvency concerns the ability of assets and loss-absorbing resources to cover liabilities and losses; a solvent institution can still face a timed cash shortage.

Long and short positions

A long position generally benefits from ownership or a rise in the relevant instrument’s value. A short position has the opposite exposure. For complex derivatives, the precise payment and sign convention should always be checked.

Maturity

Maturity is the date or remaining period until a contract ends or principal becomes due. It can differ from an instrument’s next interest-rate reset or an option’s expiry.

Model risk

Model risk is the risk of adverse decisions caused by an inappropriate model, incorrect implementation, unreliable inputs or misuse of results. Validation should examine assumptions and limitations as well as numerical correctness.

Modified duration

Modified duration measures the approximate proportional price response to a small yield change under its convention. It is distinct from contractual maturity and from supervisory duration used in SA-CCR.

Net interest income

Net interest income is interest earned on assets minus interest paid on funding over a defined period. Delta NII is the change in that income under a specified scenario relative to a baseline.

Non-maturity deposit

A non-maturity deposit has no fixed contractual final maturity of the usual term-deposit kind. Its behavioural repricing and withdrawal assumptions can differ substantially from its contractual availability to the customer.

Notional

Notional is the reference amount used to scale a financial contract’s payments or exposure measures. It is not generally the contract’s market value or the amount that would be lost on default.

Option

An option gives its holder a contractual choice, such as buying or selling an asset on specified terms. Optionality also occurs inside other products, for example when a borrower can repay early.

Payoff

A payoff is the amount a contract produces in a specified outcome, usually at exercise or maturity. Its present value is not generally equal to the payoff because timing and uncertainty also matter.

Population stability index

The population stability index compares the distribution of a variable or score across samples using defined bins. It is a diagnostic of distribution change, not a universal proof that model performance has deteriorated.

Portfolio

A portfolio is a collection of positions considered together. Its risk depends on their sizes, relationships and permitted offsets, not just the sum of their standalone risks.

PRA

The Prudential Regulation Authority is the UK prudential supervisor for the firms within its remit. PRA rules, supervisory statements and consultation proposals have different roles and legal status.

Prepayment and CPR

Prepayment occurs when principal is repaid earlier than the expected or contractual schedule. The conditional prepayment rate is an annualised measure applied to the surviving balance under the stated convention.

Present value

Present value is the value today of a future payment or stream of payments under the selected discounting assumptions. A payment received later is converted into today’s value using a discount factor.

Principal

Principal is the amount borrowed or invested before interest. A derivative’s notional principal is a reference amount used to calculate payments and may never be exchanged.

Random seed

A random seed fixes the sequence used by a pseudorandom simulation, making examples reproducible. Changing the seed generates a different sample without changing the model’s stated probability law.

Receive-fixed and pay-fixed

A receive-fixed swap position receives fixed interest and pays floating interest; a pay-fixed position does the reverse. Their value sensitivities generally have opposite signs under the same contract and market assumptions.

Reconciliation

Reconciliation compares records or results and traces differences to their source. For risk calculations, this includes trade population, valuation time, units, currency, mapping, assumptions and model version.

Regulatory capital and RWA

Regulatory capital is eligible loss-absorbing funding measured under the applicable rules. Risk-weighted assets express exposures or requirements on a risk-adjusted basis and are used with capital ratios; an exposure amount is not automatically a capital charge.

Reinvestment risk

Reinvestment risk is the risk that returned principal or income must be invested on less favourable terms. Early repayment can improve immediate liquidity while reducing future interest income.

Remediation and add-ons

Remediation addresses a model or control deficiency through documented actions. An add-on is an additional required amount under the relevant method or agreement; its basis and governance should remain separate from unexplained changes to raw sensitivities.

Risk class and bucket

A risk class groups related risk types, such as interest rates or equities. A bucket is a further prescribed grouping used in aggregation. The definitions differ across FRTB, SA-CVA and SIMM.

Risk-neutral measure

A risk-neutral measure is a pricing probability measure under which suitably discounted traded asset prices are martingales under the model’s conditions. Its probabilities are pricing weights and need not represent a real-world forecast.

Runoff

Runoff describes the amount or fraction of a funding balance assumed to leave over a specified period. A regulatory runoff rate and an internally chosen behavioural stress assumption are different inputs.

Sensitivity

A sensitivity measures how a value changes when a specified input changes, under a stated bump and unit convention. Greeks are familiar option sensitivities such as delta, gamma and vega.

Stationarity

Stationarity describes a model whose specified statistical properties remain stable over time. A stationary-curve assumption in an income example is narrower: it holds the chosen curve behaviour fixed over the projection convention.

Stress calibration

Stress calibration uses a defined adverse market period or scenario to set a model’s risk scale. The data window, factor set and aggregation method determine what the resulting stressed measure represents.

Strike

The strike is the price specified in an option for buying or selling the underlying. Its position relative to the current underlying price helps determine the option’s value and sensitivities.

Tenor

A tenor is a specified period, such as three months or five years. A curve vertex is a selected maturity point at which a rate or sensitivity is represented.

Trading book and banking book

The trading book and banking book are regulatory classifications with different risk treatments and boundary rules. They are not interchangeable labels that can be chosen solely to reduce a capital requirement.

Training, validation and test samples

Training data are used to fit a model, while validation and test data assess choices or performance outside that fitting process. An out-of-time sample helps test whether performance survives a change in observation period.

Underlying

The underlying is the asset, rate, index or other reference quantity on which a derivative’s payments depend. A derivative can depend on more than one underlying risk factor.

Variable selection

Variable selection chooses the information used by a model based on relevance, availability, stability and validation. A predictive association does not by itself show that a variable causes default or will remain useful after conditions change.

Volatility

Volatility measures the variability of a price, return or other risk factor over a stated period. It describes dispersion, not the direction in which the next move will occur.

Wholesale and retail funding

Retail funding generally comes from individual customers or qualifying small businesses, while wholesale funding comes from financial markets and larger institutional sources. Regulatory classifications and stability assumptions require more detail than these broad labels.

XVA

XVA is a collective label for valuation adjustments addressing credit, funding, collateral, capital and related effects. The adjustments must be combined consistently within a valuation framework to avoid double counting.

Yield

Yield is a rate of return implied by a price and a specified set of cash flows under a stated convention. Different yield definitions and compounding conventions can produce different numerical rates.

Yield

A yield is a rate of return implied by a price and a specified cash-flow convention. Yield to maturity is the single discount rate that equates a bond’s promised payments to its price; realised returns can differ.

Yield curve

A yield curve or term structure describes how rates or discount factors vary with maturity. Projection curves and discount curves can serve different purposes within one valuation.