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XVA

X-Value Adjustment (XVA, xVA) is an umbrella term referring to a number of different "valuation adjustments" that banks must make when assessing the value of derivative contracts that they have entered into. The purpose of these is twofold: primarily to hedge for possible losses due to other parties' failures to pay amounts due on the derivative contracts; but also to determine (and hedge) the amount of capital required under the bank capital adequacy rules. XVA has led to the creation of specialized desks in many banking institutions to manage XVA exposures.

Historically, (OTC) derivative pricing has relied on the Black–Scholes risk neutral pricing framework which assumes that funding is available at the risk free rate and that traders can perfectly replicate derivatives so as to fully hedge.

This, in turn, assumes that derivatives can be traded without taking on credit risk. During the 2008 financial crisis, many financial institutions failed, leaving their counterparts with claims on derivative contracts that were paid only in part. Therefore it became clear that counterparty credit risk must also be considered in derivatives valuation, and the risk neutral value is to be adjusted correspondingly.

When a derivative's exposure is collateralized, 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 secured lending between banks, and is thus considered a good indicator of the interbank credit markets.

When the exposure is not collateralized then a credit valuation adjustment, or CVA, is subtracted from this value (the logic: an institution insists on paying less for the option, knowing that the counterparty may default on its unrealized gain). This CVA is the discounted risk-neutral expectation value of the loss expected due to the counterparty not paying in accordance with the contractual terms, and is typically calculated under a simulation framework; see Credit valuation adjustment § Calculation.

When transactions are governed by a master agreement that includes netting-off of contract exposures, then the expected loss from a default depends on the net exposure of the whole portfolio of derivative trades outstanding under the agreement rather than being calculated on a transaction-by-transaction basis. The CVA (and xVA) applied to a new transaction should be the incremental effect of the new transaction on the portfolio CVA.

While the CVA reflects the market value of counterparty credit risk, additional Valuation Adjustments for debit, funding cost, regulatory capital and margin may similarly be added. As with CVA, these results are modeled via simulation as a function of the risk-neutral expectation of (a) the values of the underlying instrument and the relevant market values, and (b) the creditworthiness of the counterparty. This approach relies on an extension of the economic arguments underlying standard derivatives valuation.

These XVA include the following; and will require careful and correct aggregation to avoid double counting:

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