In financial mathematics one defines CVA as the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty's default. In other words, CVA is the market value of counterparty credit risk. This price adjustment will depend on counterparty credit spreads as well as on the market risk factors that drive derivatives' values and, therefore, exposure. It is typically calculated under a simulation framework.^{[4] [5] [6]} (Which can become computationally intensive; see ^[b].)

Unilateral CVA is given by the risk-neutral expectation of the discounted loss. The risk-neutral expectation can be written ^{[2] [8]} as

${\displaystyle \mathrm {CVA(T)} =E^{Q}[L^{*}]=\int _{0}^{T}E^{Q}\left[\left.LGD{\frac {B_{0}}{B_{t}}}E(t)\;\right|\;t=\tau \right]d\mathrm {PD} (0,t)}$ 

where ${\displaystyle T}$   is the maturity of the longest transaction in the portfolio, ${\displaystyle B_{t}}$  is the future value of one unit of the base currency invested today at the prevailing interest rate for maturity ${\displaystyle t}$ , ${\displaystyle LGD}$  is the loss given default, ${\displaystyle \tau }$  is the time of default, ${\displaystyle E(t)}$  is the exposure at time ${\displaystyle t}$ , and ${\displaystyle \mathrm {PD} (s,t)}$  is the risk neutral probability of counterparty default between times ${\displaystyle s}$  and ${\displaystyle t}$ . These probabilities can be obtained from the term structure of credit default swap (CDS) spreads.

Assuming independence between exposure and counterparty's credit quality greatly simplifies the analysis. Under this assumption this simplifies to

${\displaystyle \mathrm {CVA} =LGD\int _{0}^{T}\mathrm {EE} ^{*}(t)~d\mathrm {PD} (0,t)}$ 

where ${\displaystyle \mathrm {EE} ^{*}}$  is the risk-neutral discounted expected exposure (EE):

${\displaystyle \mathrm {EE} ^{*}(t)=\mathbb {E} \left\lbrack {{\frac {B_{0}}{B_{t}}}~E(t)}\right\rbrack }$ 

The full calculation of CVA, as above, is via a Monte-Carlo simulation on all risk factors; this is computationally demanding. There exists a simple approximation for CVA, sometimes referred to as the "net current exposure method".^[5] This consists in: buying default protection, typically a Credit Default Swap, netted for each counterparty; and the CDS price may then be used to back out the CVA charge. ^{[5] [9]}

The CVA charge may be seen as an accounting adjustment made to reserve a portion of profits on uncollateralized financial derivatives. These reserved profits can be viewed as the net present value of the credit risk embedded in the transaction. Thus, as outlined, under IFRS 13 changes in counterparty risk will result in earnings volatility; see XVA § Accounting impact and next section.

In the course of trading and investing, Tier 1 investment banks generate counterparty EPE and ENE (expected positive/negative exposure). Whereas historically, this exposure was a concern of both the Front Office trading desk and Middle Office finance teams, increasingly CVA pricing and hedging is under the "ownership" of a centralized CVA desk. ^{[10] [11]}

In particular, this desk addresses volatility in earnings due to the IFRS 13 accounting standard requiring that CVA be considered in mark-to-market accounting. The hedging here focuses on addressing changes to the counterparty's credit worthiness, offsetting potential future exposure at a given quantile. Further, since under Basel III, banks are required to hold specific regulatory capital on the net CVA-risk,^[5] the CVA desk is responsible also for managing (minimizing) the capital requirements under Basel.

• Financial derivative
• Potential future exposure
• XVA

• Corporate Finance Institute (N.D.). Credit Valuation Adjustment (CVA)
• Laura Ballotta, Gianluca Fusai and Marina Marena (2016). "A Gentle Introduction to Default Risk and Counterparty Credit Modelling". SSRN 281635