A textbook derivative price often assumes that payments are certain, funding is available on simple terms and trading does not consume capital or collateral resources. Real transactions involve counterparties that can default, collateral agreements, funding costs and other constraints. XVA is a collective name for valuation adjustments used to represent these effects under a specified valuation framework.

The module separates counterparty credit, own credit, funding, collateral, initial margin and capital so that you can see the economic question behind each adjustment. Later lessons examine how these effects interact with netting, wrong-way risk, clearing, reserves and tax. Several adjustments can depend on the same cash flows, which means they cannot always be calculated independently and added without checking for overlap.

Begin with the introductory valuation example and use the sign conventions shown in each lesson. Ask who is paying, who is receiving and which future cash flow is being valued. The applets illustrate mechanisms under explicit assumptions; they do not claim that every institution should use one universal XVA formula. The cited research explains the frameworks behind the more advanced examples.

Continue your learning: SA-CVA counterparty risk · SA-CCR counterparty exposure · The Standard Initial Margin Model · Treasury 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.

71 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.

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.

AVA and prudent valuation

An additional valuation adjustment recognises specified valuation uncertainty under a prudent-valuation framework. It is distinct from expected credit loss and from a trading desk’s chosen pricing adjustment.

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.

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.

CCP, default fund and CCVA

A central counterparty interposes itself between clearing participants. Its default fund supports the specified loss-allocation arrangements. CCVA denotes the clearing-related valuation adjustment in the relevant lesson, whose components are defined by the cited model.

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.

Collateral and liquidity valuation adjustments

Collateral and liquidity valuation adjustments represent the value effects of collateral remuneration or related liquidity and financing differences under a stated framework. Their labels and boundaries are not universal across institutions.

ColVA

Collateral valuation adjustment captures the valuation effect of collateral remuneration or funding terms relative to the clean pricing benchmark in the chosen framework. Its treatment must be consistent with the other funding adjustments to avoid double counting.

Compounding

Compounding describes how interest accumulates on principal and previously earned interest. Under continuous compounding, accumulation is represented by an exponential function rather than a sequence of periodic additions.

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 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.

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.

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.

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.

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.

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.

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.

FVA, FCA and FBA

Funding valuation adjustment represents the relevant funding effects in a valuation framework. Funding cost adjustment and funding benefit adjustment distinguish cost and benefit components, subject to the model’s treatment of collateral and own credit.

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.

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.

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.

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.

KVA

Capital valuation adjustment represents the value of the cost of supporting a trade or portfolio with capital under a specified framework. It depends on future capital requirements, remuneration assumptions and valuation conventions.

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.

MVA

Margin valuation adjustment represents the value of funding initial margin over the relevant future life of a portfolio. It depends on projected margin and funding assumptions, not just the initial margin balance today.

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.

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.

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.

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.

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.

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.

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.

RAROC and economic capital

Risk-adjusted return on capital compares the specified risk-adjusted income with allocated capital. A hurdle is the required return used in the decision. Economic capital is an internal risk-based measure and need not equal regulatory capital.

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.

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.

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.

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-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.

Segregation

Segregation separates collateral or assets under specified legal arrangements. Bankruptcy-remoteness and permitted reuse depend on the actual structure, so received initial margin cannot automatically be assumed available to fund posted margin.

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.

SIMM and ISDA

The Standard Initial Margin Model is ISDA’s sensitivity-based model for initial margin on the relevant derivatives portfolios. ISDA is the International Swaps and Derivatives Association, which publishes the identified methodology and related standards.

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.

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.

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.

TVA

Tax valuation adjustment represents tax-related effects included by a specified valuation framework. The relevant treatment depends on the jurisdiction, cash flows and assumptions rather than a universal add-on percentage.

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.

Variation margin

Variation margin addresses changes in current exposure by transferring collateral according to the agreement. A received or posted amount is a cash or collateral flow, not an additional valuation profit by itself.

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.

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 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.