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Credit Valuation Adjustment

Credit Valuation Adjustment (CVA) is a tool in counterparty credit risk management and its application. Counterparty credit risk is the risk that a counterparty to a financial contract will default prior to expiry, failing to make future contracts and resulting in a credit exposure to the financial institution. Traditional methods of managing counterparty credit risk include netting agreements and collateralization to reduce the overall exposure to a single counterparty. Over the past decade, institutions have also used Credit Default Swap (CDS) protection to manage exposures

CVA, by definition, is the difference between the risk-free portfolio value and the true (or risky or defaultable) portfolio value that takes into account the possibility of a counterparty’s default. The risk-free portfolio value is what brokers quote or what trading systems or models normally report. The risky portfolio value, however, is a relatively less explored and less transparent area, which is the main challenge and core theme for CVA. In other words, central to CVA is risky valuation.

In the market, risk-free values are quoted for most financial derivatives. In other words, credit risk is not captured. Historical experience shows that credit risk often leads to significant losses. Therefore, it is obvious to all market participants that credit risk should be taken into account when reporting the fair value of any defaultable derivative. The adjustment to the risk-free value is known as the credit value adjustment (CVA).

More informally, think of CVA as the fair value of buying protection against the counterparty’s potential failure to meet contractual obligations. From this perspective, calculation of CVA is a pricing exercise similar to option pricing. In particular, because we are interested in the fair value of protection we can express the problem as the cost of hedging against default, allowing us to work in a risk-neutral measure in which the expected return of the hedged portfolio is the risk-free rate.

For completeness, our theoretical study covers various cases. We find that the valuation of defaultable derivatives and their CVAs, in most situations, has a backward recursive nature and requires a backward induction valuation. An intuitive explanation is that two counterparties implicitly sell each other an option to default when entering into a defaultable transaction. If we assume that a default may occur at any time, the default options are American style options. If we assume that a default may only happen on the payment dates, the default options are either European options or Bermudan options. Both Bermudan and American options require backward induction valuations.



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