A derivative is a promise to exchange future payments. If the counterparty fails when it owes the bank money, the bank may not recover the full amount. Credit valuation adjustment, or CVA, reduces a default-free valuation to reflect this expected loss. CVA can change before any default occurs because the counterparty’s credit spread or the market factors driving exposure have changed.

This module first explains CVA itself, including future positive exposure, credit curves, netting, collateral and wrong-way risk. It then introduces the standardised approach to CVA risk capital, or SA-CVA. That capital calculation measures sensitivity to changes in CVA and eligible hedges; it is a different quantity from the current CVA valuation adjustment or the capital held against counterparty default exposure.

The six risk-class laboratories show how sensitivities and eligible hedges are weighted and aggregated. As you use them, check whether you are changing a valuation input, a hedge or a regulatory calculation input. Finish with the total-capital and governance lessons to understand how the pieces fit together. The examples follow the cited PRA provisions and state the factors and assumptions omitted from each reduced portfolio.

Continue your learning: SA-CCR counterparty exposure · XVA valuation adjustments · Risk sensitivities

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.

67 definitions

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.

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.

Bootstrapping

Bootstrapping builds a curve sequentially by using market instruments to determine additional discount factors or rates once earlier points are known. The result depends on instrument selection and pricing conventions.

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.

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.

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.

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 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.

DVA

Debit valuation adjustment reflects the effect of the bank’s own default risk on the value of its obligations under a bilateral valuation framework. It is not an amount of cash that can automatically be used to fund a position.

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 positive exposure

Positive exposure is the amount at risk when the counterparty owes the bank money in a specified state. Expected exposure averages positive exposure across scenarios at a time; expected positive exposure is also used in regulatory contexts for a specified time average, so the exact definition must be checked.

Finite difference

A finite difference estimates a sensitivity by repricing after a small change in an input. The bump size, direction and units determine how the observed price change is converted into a sensitivity.

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.

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.

Hazard rate

A default hazard rate describes the instantaneous rate of default conditional on survival up to that time. A spread divided by LGD is a simplified hazard approximation, not a full credit-curve calibration.

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.

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.

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.

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.

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.

Margin period of risk

The margin period of risk is the period over which exposure can change between the relevant collateral snapshot and effective close-out or replacement. Operational delays and contractual conditions can affect its required treatment.

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.

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.

Percentage point

A percentage point is the arithmetic difference between two percentages. An increase from 2% to 3% is one percentage point, but it is a 50% relative increase.

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.

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.

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.

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.

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-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.

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.

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.

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.

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.

Standard deviation

Variance is the probability-weighted squared deviation from a mean. Standard deviation is its square root and is expressed in the original units of the variable.

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.

Survival probability

Survival probability is the probability that default has not occurred by a specified time. Its decline across an interval gives the probability of first default during that interval under the model.

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.

Threshold and MTA

A threshold defines an amount that may remain unsecured or uncollateralised under the applicable arrangement. A minimum transfer amount limits small collateral transfers. Their legal scope and treatment differ across regulatory and contractual contexts.

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.

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.

Wrong-way risk

Wrong-way risk occurs when exposure increases in conditions associated with a greater likelihood or severity of counterparty loss. Right-way dependence moves in the opposite direction, but the model and evidence must establish the relationship.

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.