XVA

An X-Value Adjustment (XVA) is a generic term referring collectively to a number of different “Valuation Adjustments” in relation to derivative instruments held by banks.^[1][2]

The context^[3][4][5] is that, historically, (OTC) derivative pricing has relied on the Black-Scholes' risk neutral pricing framework, under the assumptions of funding at the risk free rate and the ability to perfectly replicate derivatives so as to fully hedge; see Black–Scholes equation § Derivation; Rational pricing § The replicating portfolio. This, in turn, is built on the assumption of a credit-risk-free environment. Post the financial crisis of 2008, therefore, counterparty credit risk must also be considered in the valuation,^[6] and the risk neutral value is then adjusted correspondingly. The purpose of this calculation is twofold: primarily to hedge for possible losses due to counterparty default; but also, to determine (and hedge) the amount of capital required under Basel III. See Financial economics § Derivative pricing for further context. For a discussion as to the impact of xVA on the bank's overall balance sheet, return on equity, and dividend policy, see: ^[5].

The approach to these calculations in overview: When the deal is collateralized then the "fair-value" is computed as before, but using the Overnight Index Swap (OIS) curve for discounting. (The OIS is chosen here as it reflects the rate for overnight unsecured lending between banks, and is thus considered a good indicator of the interbank credit markets.) When the deal is not collateralized then a CVA – credit valuation adjustment – is added to this value; ^[3] essentially, the risk-neutral expectation of the discounted loss due to the counterparty not performing.

While the CVA reflects the market value of counterparty credit risk, additional Valuation Adjustments for Debit, Funding, regulatory capital and margin may similarly be added.^[7][8] Note that this has required the creation of specialized desks,^[9] and requires careful and correct aggregation without double counting.^[4]

These adjustments:^[10]

• DVA, Debit Valuation Adjustment: analogous to CVA, an adjustment to a derivative price based on the institution's own default risk.
• FVA, Funding Valuation Adjustment, due to the funding implications of a trade that is not under a perfect Credit Support Annex (CSA); essentially the difference between the rate paid for the collateral to the bank's treasury, and the rate paid by the clearinghouse:
  • FVA = FVA receivables + FVA payables = FCA + FBA, where FCA is due to self funded borrowing spread over Libor, and FBA due to self funded lending.
• KVA, the Valuation Adjustment for regulatory capital through the life of the contract.
• MVA, Margin Valuation Adjustment, refers to the costs specific to centrally cleared transactions, such as adjustments for initial margin and variation margin.

Other adjustments are also sometimes made ^[7] including TVA, for tax, and RVA, for replacement of the derivative on downgrade.

As for CVA, these results are modeled as a function of the risk-neutral expectation of (a) values of the underlying instrument, and (b) creditworthyness of the counterparty; typically this is under a simulation framework.

References

Bibliography

• Andrew Green (2015). XVA: Credit, Funding and Capital Valuation Adjustments. Wiley. ISBN 978-1-118-55678-8. 
• Jon Gregory (2015). The xVA Challenge: Counterparty Credit Risk, Funding, Collateral, and Capital (3rd Edition). Wiley. ISBN 978-1-119-10941-9. 
• Ignacio Ruiz (2015). XVA Desks - A New Era for Risk Management. Palgrave Macmillan UK. ISBN 978-1-137-44819-4.