CVA as Expected Counterparty Default Loss on Derivatives
Summary
The document explains credit valuation adjustment (CVA) through an unsecured derivatives portfolio. If the portfolio has positive value when a counterparty defaults, the surviving party may recover only part of the close-out amount, with the recovered share depending on the recovery rate. CVA represents the risk-neutral expected cost of this counterparty credit exposure, or the market cost of hedging it.
A second answer disputes the idea that CVA is simply a derivative or a directly hedgeable position at inception. It frames CVA and debit valuation adjustment as marginal costs created by counterparty credit risk and says contingent credit default swaps can approximate that exposure. The discussion is conceptual: it gives no calculation method, numerical example, or evidence comparing valuation approaches, and the answers present differing emphases on CVA's interpretation and hedgeability.
Key ideas
- CVA reflects potential losses on positive-value derivatives if a counterparty defaults.
- Recovery rates determine how much of a close-out amount may be recovered.
- CVA can be understood as a risk-neutral expected credit loss or the market cost of hedging that risk.
- One answer characterizes CVA and DVA as marginal credit costs and describes contingent credit default swaps as an approximation.
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Full text
# What is CVA (credit valuation adjustment)? # What is CVA (credit valuation adjustment)? According to Wikipedia, CVA is defined 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. What does the 'risk-free portfolio value' mean? I guess it's similar to the risk premium (risky asset return - riskfree asset return), but can anyone provide an example of the risk-free portfolio value in the context of CVA? Thank you. ## Answer by Adam N. (score 2, accepted) https://quant.stackexchange.com/a/35472 If you have a portfolio of derivatives with a counterparty and this counterparty defaults before the trades mature, the net mark to market value of the portfolio will be calculated according to the master agreement and a close-out amount will be supposed to be paid by one party to the other. If this portfolio has a positive mark to market value (from your point of view), you won't be able to recover the full amount in the insolvency proceedings, but rather only a part of it (determined by the recovery rate). This means there's a probability that you incur a loss, due to counterparty credit risk. CVA is basically the (risk-neutral) expected value of this loss, or equivalently the price of hedging this risk in the market. ## Answer by achirikhin (score 1) https://quant.stackexchange.com/a/79309 Wikipedia is wrong. CVA/DVA is the cost of the marginal credit (counterparty) risk created when a (partially) unsecured derivative is traded. It is not a derivative and not hedgeable at inception. The mainstream approach is to approximate it by a contingent CDS (CCDS), which actually IS a derivative.
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