XVA: An Introduction to Valuation Adjustments#

XVA is the family of valuation adjustments applied to a derivative portfolio to reflect the costs and risks that sit outside the plain risk-free mark. In a modern OTC derivatives book, the clean market value is rarely the whole story. A price that ignores counterparty credit, funding, liquidity and capital can materially understate or overstate the economic value of a trade.

The term XVA is a shorthand for several related adjustments, including CVA, DVA, FVA and KVA. Together they translate the economics of credit, funding and regulatory capital into the valuation and risk numbers used by trading, control and treasury functions.

In practice, XVA matters because derivative valuations are not just a question of discounting cash flows. They also reflect the actual cost of hedging and the risk of loss or benefit associated with default, funding and regulatory capital. For banks, these effects can be material on large portfolios and are therefore part of both pricing and risk management.

The main XVA terms#

The main XVA adjustments#

Adjustment

Name

Typical meaning

CVA

Credit Valuation Adjustment

The cost of counterparty default risk. It reduces the value of a derivative when the counterparty might fail to pay.

DVA

Debit Valuation Adjustment

The benefit to the institution from its own default risk. It reflects the fact that a bank may owe money to a counterparty, and the counterparty may not be fully repaid if the bank defaults.

FVA

Funding Valuation Adjustment

The cost of funding the derivative position, including differences between risk-free funding and the institution’s actual funding rate.

KVA

Capital Valuation Adjustment

The cost of holding regulatory capital against the trade and the related economic burden of capital requirements.

Why XVA is important#

XVA is central to how banks manage derivative portfolios because it connects valuation with the real economic constraints of the business. A desk may price a trade at a level that looks attractive on a simplified mark, but the firm may be exposed to substantial credit, funding and capital costs that are not yet reflected. Those effects matter for:

  • pricing and trade negotiation

  • fair value reporting and controls

  • hedging and balance sheet management

  • covenant and capital planning

  • risk appetite and limit setting

The core idea is simple: a derivative is not just a stream of future cash flows. It is also a package of exposures to default, funding and capital costs. XVA is the mechanism for adjusting the value to reflect those exposures.

Other adjustments#

CVA, DVA, FVA and KVA are the core adjustments, but the XVA family is wider. Other adjustments seen in practice include:

Other valuation adjustments#

Adjustment

Name

Typical meaning

MVA

Margin Valuation Adjustment

The cost of funding initial margin posted over the life of the trade, most relevant for centrally cleared and bilateral margined derivatives. See MVA: Margin Valuation Adjustment.

ColVA

Collateral Valuation Adjustment

The value of optionality embedded in a collateral agreement, for example the right to choose which currency or asset to post. See ColVA: Collateral Valuation Adjustment.

TVA

Tax Valuation Adjustment

The impact of tax on the cash flows and on the other adjustments. See TVA: Tax Valuation Adjustment.

Not every institution calculates every adjustment. Which ones are charged, reserved or simply monitored depends on the business model, the accounting policy and the market practice for each product.

Exposure concepts#

Most XVA calculations are built on the exposure of a portfolio to a counterparty. Exposure is the amount the firm would lose if the counterparty defaulted, and it only exists when the portfolio value is positive to the firm. The key measures are:

Exposure measures#

Measure

Meaning

Exposure

The positive part of the portfolio value, \(\max(V, 0)\), at a future date.

EE

Expected Exposure: the average exposure at a future date across simulated scenarios.

EPE

Expected Positive Exposure: the average of the expected exposure over time.

ENE

Expected Negative Exposure: the mirror image of EE, the exposure the counterparty has to us. It drives DVA.

PFE

Potential Future Exposure: a high percentile (for example 95% or 99%) of the exposure distribution. It is used for limits rather than for valuation.

CVA, DVA and FVA are all calculated from these exposure profiles, so the quality of the exposure simulation drives the quality of the XVA numbers.

Netting sets#

Exposure is not measured trade by trade. Under a legally enforceable netting agreement, such as an ISDA master agreement, the trades with a counterparty are netted into a single net amount on default. The set of trades covered by one agreement is a netting set. Netting can reduce exposure significantly, so XVA must be calculated at the netting set level and then allocated back to trades or desks.

Collateral and CSAs#

A Credit Support Annex (CSA) to the ISDA agreement sets out when and how collateral is exchanged. Variation margin is posted as the mark-to-market moves, which reduces the current exposure. Initial margin is posted upfront to cover the potential move during the close-out period.

Collateral reduces XVA but does not remove it. Reasons include:

  • the margin period of risk: it takes time, typically around ten days, to close out and replace a defaulted counterparty, and the market can move in that window

  • thresholds and minimum transfer amounts, which leave some exposure uncollateralised

  • disputes and operational delays in calling and receiving margin

  • the quality and liquidity of the collateral itself

  • the cost of funding the collateral, which is the source of FVA and MVA

Uncollateralised trades, for example with corporates, carry the largest XVA because the whole exposure is open.

Wrong-way risk#

Standard CVA models assume that the exposure and the counterparty’s default probability are independent. Wrong-way risk is the case where they are not: the exposure increases as the credit quality of the counterparty deteriorates.

Examples include:

  • buying protection on a bank from a counterparty that is itself a bank in the same system

  • a cross-currency swap with a counterparty whose home currency weakens sharply as its credit worsens

  • a derivative on a commodity with a producer whose creditworthiness depends on the commodity price

Wrong-way risk increases CVA and is hard to model because it requires the dependence between market factors and credit to be specified. It is usually handled with stressed correlations, scenario analysis or add-ons to the standard calculation. Right-way risk is the opposite case, where the exposure falls as the credit worsens.

How XVA is calculated#

The usual approach is a Monte Carlo simulation of the market risk factors that drive the portfolio value:

  1. Simulate many paths of the relevant risk factors (rates, FX, equity, credit and so on) over the life of the longest trade.

  2. Revalue every trade in the netting set at each future date on each path, including the effect of collateral.

  3. Aggregate to the exposure profiles (EE, ENE and so on) at each date.

  4. Combine the profiles with credit spreads, recovery rates and funding spreads to produce each adjustment.

  5. Calculate the sensitivities (Greeks) to the inputs, so that the adjustments can be hedged and explained.

This is computationally heavy. A large portfolio can have many thousands of trades, hundreds of dates and thousands of paths, and the sensitivities multiply the cost again. Banks therefore use techniques such as algorithmic differentiation for the sensitivities, GPUs, and approximations that replace full revaluation of each trade by a regression on the simulated state (the Longstaff-Schwartz approach).

The XVA desk and hedging#

Many banks manage XVA centrally in an XVA desk. The desk:

  • charges the trading desks for the XVA on each new trade, so that it is in the price quoted to the client

  • takes on the resulting credit, funding and capital risk and manages it as a portfolio

  • hedges the market risk of the exposure, for example interest rate and FX delta, so that the exposure profile does not move the P&L

  • hedges the credit spread risk of CVA, using single-name or index credit default swaps where liquid

Some risks cannot be hedged well. Own-credit risk (DVA) cannot be hedged directly, many counterparties have no liquid credit protection, and the exposure itself changes with the market. The unhedged part is a source of P&L volatility that the desk and the control functions need to understand.

Accounting and regulation#

Under IFRS 13 and US GAAP (ASC 820), derivatives are carried at fair value, which is the exit price a market participant would pay. This is why credit and, increasingly, funding adjustments are included in the reported value.

  • CVA and DVA are widely accepted components of fair value.

  • FVA is accepted by most large banks but the treatment is less uniform. There is a continuing debate about whether it is a genuine cost or double counts the benefit already captured in DVA.

  • KVA is generally treated as a management and pricing tool rather than a component of reported fair value (see KVA: Capital Valuation Adjustment).

Regulatory capital adds a further layer. Under Basel III the CVA capital charge covers the risk of mark-to-market losses on the CVA, and it is calculated using either the standardised approach (SA-CVA) or a basic approach (BA-CVA). Gains from the firm’s own credit (DVA) are removed from regulatory capital, so DVA gives no capital benefit. Under IFRS 9, the own-credit movements on liabilities designated at fair value are taken to other comprehensive income rather than P&L.

A valuation control view#

For the valuation control function, XVA is a source of valuation uncertainty and judgement, so it falls inside the independent price verification and reserves framework. The typical areas of challenge are:

  • Inputs: credit spreads, recovery rates and funding curves are often illiquid or proxied for many counterparties. Controls test the proxy mapping and compare to observable data where it exists.

  • Models: independent model validation checks the exposure simulation and the wrong-way risk treatment, and the results are benchmarked against alternative implementations.

  • Reserves and methodology: judgement on the funding assumptions, the FVA treatment and the model limitations may require a reserve or a model adjustment.

  • Completeness: every trade and netting set, with its collateral terms, must feed the calculation. Missing or incorrect trade attributes (such as CSA terms) are a common source of error.

  • Explain: the daily XVA movement is attributed to market moves, new trades, the roll of time and model or data changes, so that unexplained moves are investigated.

  • Governance: the methodology, the allocation of XVA to desks and any overrides are documented and approved through the valuation governance forums.

These are the same themes as for any other level 2 or level 3 valuation: independent data, a challenged methodology, and a clear explain of the P&L.

This series#

This series introduces the main concepts behind XVA and explains how each adjustment is interpreted in practice. The next sections cover the principal components in more detail: