The Fundamental Review of the Trading Book, usually called FRTB, is a framework for measuring the capital a bank needs against market risk in its trading book. Market prices can move, issuers can default, and some payoffs carry risks that ordinary sensitivities do not describe well. The framework therefore uses several components rather than treating every possible loss as the same problem.

The standardised approach begins with sensitivities-based capital for delta, vega and curvature risk. It also includes a default risk charge and a residual risk add-on. You will explore the risk classes, see how positions are assigned to buckets, and follow the effect of weights, correlations and permitted offsets. The trade explorer connects familiar instruments to the components that may capture their risks.

The internal models approach uses a different calculation route and requires supervisory permission. Its lessons cover expected shortfall, liquidity horizons, stress calibration, modellability, data quality, profit-and-loss attribution and backtesting. These tests matter because a plausible model result alone does not establish that a desk is eligible to use the approach.

Start with the capital map, then work through the standardised calculations before moving to the internal models lessons. The module uses the identified PRA instrument as its principal reference and explains the scope of each example. A model input, an internal assumption and a prescribed regulatory parameter are distinguished throughout. The separate regulation module lets you compare the selected PRA, US proposal and Basel documents.

Continue your learning: Risk sensitivities · FRTB Regulation Divergences · The Standard Initial Margin Model

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.

120 definitions

ABS, RMBS and CDO

Asset-backed securities are backed by a pool of assets. Residential mortgage-backed securities are backed by residential mortgages. A collateralised debt obligation divides exposure to a debt portfolio into tranches under its structure.

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.

Alternative correlation trading portfolio

The alternative correlation trading portfolio is a defined FRTB category with specific eligibility and calculation rules. Securitisation positions outside that category receive a different treatment; a model user cannot assign membership solely to obtain a preferred charge.

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.

At the money

An option is at the money when its strike is close to the relevant underlying price or forward price under the stated convention. Moneyness describes that relationship more generally.

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.

Barrier

A barrier is a specified level whose crossing changes a contract’s payoff or ends a stopping-time experiment. Crossing risk depends on the path, not only the final value.

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.

Carry and opportunity cost

Carry is the ongoing income or expense from holding and financing a position. Opportunity cost compares that choice with a specified alternative, whose credit, capital and liquidity risks may differ.

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.

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.

Conditional, marginal and cumulative PD

Conditional PD applies to borrowers still surviving at the start of an interval. Marginal PD is the probability of first default during that interval from the original population, while cumulative PD is the probability of default by a specified date.

Constrained and unconstrained expected shortfall

Unconstrained expected shortfall reflects the permitted joint-portfolio calculation. The constrained component restricts diversification across broad risk classes. The FRTB models-based capital calculation combines the specified measures rather than allowing arbitrary diversification assumptions.

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.

Credit default swap

A credit default swap exchanges a protection premium for a contractual payment if a specified credit event occurs. The protection buyer generally benefits when the reference credit deteriorates, subject to the contract’s terms.

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.

Credit-spread risk

Credit-spread risk is the risk of value changes caused by movements in credit spreads. FRTB distinguishes non-securitisation, securitisation outside the alternative correlation trading portfolio and alternative correlation trading portfolio treatments.

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.

Default risk charge

The default risk charge is the FRTB capital component addressing issuer default losses. Its calculation is distinct from ordinary price sensitivities and from counterparty exposure on a derivative.

Delta

Delta is the first-order sensitivity of value to a specified underlying input. A delta hedge offsets that local exposure at the current point but may need adjustment when the market moves.

Discount factor extrapolation

Extrapolation estimates a curve beyond its observed maturities. Unlike interpolation, it extends outside the available data and can make long-dated values particularly sensitive to the chosen assumptions.

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.

Diversification

Diversification is the reduction in aggregate risk that can arise when positions do not experience adverse outcomes together. Its benefit depends on the chosen risk measure, dependence assumptions and any regulatory aggregation rules.

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.

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.

Expected loss

Expected loss is the probability-weighted average loss over a defined set of outcomes. In a simple single-period credit example it is PD multiplied by LGD and EAD, but richer models also account for timing and dependence.

Expected shortfall

Expected shortfall averages losses in a specified worst part of the loss distribution. Its treatment of probability mass at the threshold matters for discrete scenario samples.

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.

FRTB

FRTB stands for the Fundamental Review of the Trading Book. It is the market-risk capital framework covered in the selected Basel and jurisdictional documents, including standardised and internal-models approaches.

Full and reduced factor sets

FRTB internal-models calculations distinguish a full risk-factor set from a reduced set used for stress calibration. Labels such as FC and RC in the applets refer to full-current and reduced-current measures; RC in SA-CCR instead means replacement cost. PES labels the supplied partial expected-shortfall inputs in the relevant FRTB lesson.

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.

General interest-rate risk

GIRR is the FRTB risk class for general interest-rate factors, including the specified curve, inflation and cross-currency basis risks. It is distinct from credit-spread risk.

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.

Idiosyncratic and systematic risk

Idiosyncratic risk is specific to a name or position, while systematic risk is driven by factors shared across many positions. The distinction affects diversification assumptions and some regulatory aggregation treatments.

Implied volatility

Implied volatility is the volatility parameter that makes a selected pricing model match an observed option price. A volatility smile or surface describes how implied volatility varies across strikes and expiries.

Incremental and standalone risk

Standalone risk measures a position by itself. Incremental risk is the change in portfolio risk when the position is added; it can be negative when the new position hedges an existing exposure.

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.

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.

Internal models approach

The internal models approach uses approved internal risk models within regulatory constraints. Model output alone does not establish eligibility; permission, data quality and ongoing tests also matter.

Interpolation

Interpolation supplies values between known curve points. Linear interpolation in rates and linear interpolation in logarithms of discount factors need not produce the same intermediate prices or sensitivities.

Intraday liquidity

Intraday liquidity is the ability to meet payment and settlement obligations during the day. A positive closing cash balance can hide an earlier shortage if outgoing payments precede incoming funds.

Investment grade and high yield

Investment grade and high yield are credit-quality groupings based on the relevant rating or classification rules. Rating labels such as AA and BBB indicate categories, not guarantees of repayment.

Jump to default

Jump to default measures the relevant change in value or loss if the reference issuer defaults, under the framework’s conventions. Eligible netting, maturity scaling, seniority and caps can affect the amount used in capital.

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.

Liquidity horizon

A liquidity horizon is the period used to represent how long risk may take to hedge or close under the applicable framework. FRTB liquidity-horizon adjustments are not interchangeable with an arbitrary scaling of a portfolio VaR.

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.

Netting set

A netting set contains transactions that can be combined under the relevant legally recognised agreement and calculation rules. Economic offsets across different legal sets do not automatically qualify as regulatory or collateral offsets.

Non-modellable risk factor

A non-modellable risk factor does not meet the applicable modellability requirements for the ordinary internal-model calculation. Its risk is addressed through the specified stressed treatment rather than ignored.

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.

OTC and clearing

An over-the-counter derivative is negotiated outside a traditional exchange trading arrangement. Clearing through a central counterparty changes counterparty and collateral arrangements; an OTC trade may be centrally cleared or remain bilateral.

Par rate

A par rate is the coupon or fixed rate that makes an instrument’s value equal to its stated par value, or makes a swap have zero initial value, under the specified valuation conventions.

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.

Poisson process

A Poisson process counts randomly timed events with a specified intensity under its assumptions. Adding jumps allows a model to represent discontinuous changes that a purely continuous diffusion cannot generate.

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.

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.

Probability of default

Probability of default is the probability that a borrower defaults over a defined horizon and under specified conditions. One-year, remaining-lifetime, market-implied and prudential PDs answer different questions.

Profit-and-loss attribution

Profit-and-loss attribution compares risk-theoretical P&L with hypothetical P&L to assess whether the model captures the desk’s relevant risk drivers. Its eligibility consequences and thresholds depend on the applicable rules.

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.

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.

Recovery and LGD

Recovery is the amount obtained after default, taking account of the relevant cash flows and costs. Loss given default, or LGD, is the fraction of exposure lost under the selected timing and discounting convention.

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.

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.

Replacement cost

Replacement cost is the current exposure component in SA-CCR under the applicable netting and collateral rules. Current market value, or CMV, is an input; replacement cost need not equal an unadjusted positive trade value.

Replication and no-arbitrage

Replication constructs a portfolio with the same payoffs as a claim in the modelled states. No-arbitrage requires matching attainable payoffs to have consistent prices under the relevant financing and trading assumptions.

Repo

A repurchase agreement raises cash against securities under an agreement to reverse the transaction. It creates a funding and repayment relationship and differs from an outright asset sale.

Residual risk add-on

The residual risk add-on is the FRTB standardised charge for specified risks that the other components do not adequately capture. Its prescribed gross-notional basis and exemptions differ from ordinary sensitivity netting.

Revolving facility

A revolving facility allows borrowing, repayment and further drawing within contractual terms. Its exposure and expected life can depend on customer behaviour and the lender’s ability to mitigate credit risk.

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 factor

A risk factor is a market or credit quantity whose movement affects a position’s value or loss. Examples include an interest rate, an exchange rate, a credit spread and an implied volatility.

Risk factor eligibility test

The risk factor eligibility test assesses whether a risk factor has sufficient qualifying real-price observations to be treated as modellable under the relevant rules. Observation dates and mapping matter, not just the annual count.

Risk weight and weighted sensitivity

A risk weight scales a relevant exposure or sensitivity according to the framework. A weighted sensitivity retains the required sign and is then combined with other weighted sensitivities under the applicable aggregation rules.

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.

RMS error

Root mean square error summarises the size of a set of differences by squaring them, averaging and taking a square root. It is non-negative and is expressed in the original measurement units.

SA-CCR

SA-CCR is the standardised approach for counterparty credit risk. It combines replacement cost and potential future exposure, with the relevant alpha treatment, to produce a regulatory exposure-at-default amount.

SA-CVA and BA-CVA

SA-CVA is the standardised approach to CVA risk capital and uses the relevant sensitivities and eligible hedges. BA-CVA is the basic approach under its own rules. Permissions and portfolio scope determine which treatment applies.

Securitisation and tranche

A securitisation allocates cash flows and credit losses from a pool of exposures to securities or positions. A tranche has a specified priority and loss-absorption range, so its risk can differ substantially from the average risk of the pool.

Seniority

Seniority describes a claim’s priority relative to other claims on an issuer. It affects recovery and can determine whether positions are permitted to offset in a default-risk calculation.

Sensitivities-based method

The sensitivities-based method is the FRTB standardised component for delta, vega and curvature risk. It weights and aggregates relevant sensitivities and repricing effects using the applicable bucket and correlation rules.

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.

Spearman and KS statistics

Spearman correlation compares the rank ordering of observations. The Kolmogorov–Smirnov statistic compares empirical cumulative distributions. Neither statistic alone explains the economic source of a model discrepancy.

Spot price

The spot price is the price or exchange rate for a transaction with the usual near-term settlement convention. It differs from a forward price agreed for a later transaction.

Standardised approach

A standardised approach uses prescribed calculation structures and parameters, although some inputs still come from the bank’s portfolio and systems. The precise meaning depends on whether the framework concerns market risk, counterparty exposure or another risk.

Standardised fallback and CU

A standardised fallback applies the prescribed standardised treatment to positions or desks that are not eligible for the internal-model route. CU denotes the standardised charge for ineligible desks in the specific FRTB capital example, with its scope stated there.

Stress and reverse stress testing

Stress testing examines the effect of specified adverse conditions. Reverse stress testing starts with an unacceptable outcome and asks what conditions could cause it, without automatically assigning those conditions a probability.

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.

Stressed NMRF charge

The stressed risk measure for non-modellable factors estimates their capital contribution under the applicable stress and aggregation rules. The selected documents use different labels, including SSRM and stressed expected shortfall, so the cited definition must be checked.

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.

Twelve-month and lifetime ECL

Twelve-month ECL concerns lifetime cash shortfalls associated with defaults that are possible in the next twelve months. Lifetime ECL concerns defaults possible over the relevant expected life; twelve-month ECL is not simply the next year’s missed payments.

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.

Value at Risk

Value at Risk is a loss threshold at a chosen confidence level over a specified horizon. It does not describe how severe losses beyond that threshold may be. A quantile is the corresponding threshold in a probability distribution.

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.

Vega

Vega measures how value changes with the volatility input of a pricing model. A vega quoted per one volatility percentage point differs by a factor of 100 from a derivative taken with respect to volatility expressed as a decimal.

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.

Volatility smile and skew

A volatility smile or skew describes how quoted implied volatility varies across strikes for a given expiry. Using one constant volatility omits this market pattern and can miss risk when the pattern changes.

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.