CVA, or Credit Value Adjustment, is an additional charge that a client must pay for a derivatives transaction, to compensate their counterparty for the fact that they are not risk free and may default on obligations which arise from the derivatives contract.

The easiest way to illustrate CVA is through a risky bond transaction (though this is standard credit risk, and not strictly speaking CVA). The bondholder will pay the bond issuer less for a credit risky bond than they would have paid for a bond which was risk free. If the bondholder enters into a CDS contract to guarantee the notional repayment on the bond, the bondholder will now pay away a portion of their coupons in return for credit protection on the bond. The total value of the bond, with the reduced coupon, is equal, under risk free discounting, to the price paid by the bondholder for the bond.

Put another way, the issuer, for a bond on which they would receive the same price, could have paid the bondholder lower coupons, if they were a risk free issuer. The higher coupons due to credit risk, can be thought of as the CVA charge.

Let’s take a step back, and get into what CVA is, and why it’s important, to the bank, and in the Basel III regulatory framework. Once again, we’ll center the discussion around the regulatory formulation of CVA :

Which equates to

 – The prevailing market view of Loss Given Default on the counterparty

– The counterparties credit spread trading for time

– The expected exposure, against the relevant counteprarty, if there were to be a default at time

– The discount factor from time until the current date.

This is an approximation of the formula you’ll find on the CVA Wikipedia page.

The institution enters into a credit risky derivatives transaction with a counterparty. The counterparty will pay a CVA charge as part of the transaction. This charge is then allocated to the CVA desk who are tasked with hedging the transaction against associated credit risk. This hedge is entered into to hedge both changes in the credit quality, as well as default by the counterparty. Ignoring the expected exposure for now, and focussing on the probability of default/credit spread portion of the equation, the transaction will be marked-to-market on a daily basis, along with it’s associated CVA charge. This is now the CVA that should be paid if the transaction were to be entered into today. If the credit quality of the counterparty were to decline, their PD would increase, and the mark-to-market CVA charge would be higher, meaning that the positions value decreases. Likewise, if the counterparties credit quality improved, the positions value would increase, as the CVA paid for the trade will be greater than the CVA required to enter into the same trade today. Hedging the CVA (e.g. buying protection through a CDS) can hedge the position against these changes in value due to changing credit quality.

Basel III requires a capital charge for the VaR associated with CVA. This is calculated by running the specific risk (issuer spreads) VaR scenarios and calculating VaR on the CVA’s mark-to-market (assuming the expected exposures are a pre-calculated input). Elligible hedges for this charge are variations of CDSs and other hedging instruments which reference the counterparty directly. Only trades specifically booked to hedge CVA can be included in the CVA VaR calculation. One thus reduces the capital charge on a trades CVA, by hedging appropriately with a CDS for example (buying credit protection). Assuming the expected exposure is matched exactly, change in the spreads will lead to the same change in value in the CDS and CVA, and VaR will be 0 for the hedged position.

The CVA desk must determine the appropriate charge for derivatives transactions. If the transaction is entered into, and CVA is paid, the desk is then responsible for hedging the position to minimise the pnl due to changes in the counterparties creditworthiness. If a good CVA price is paid, and the position is well hedged, the desk will profit from the CVA charge.

From a regulatory perspective, it is important that institutions hold capital to cover deterioration of value of their portfolios in the case that creditworthiness of their counterparties declines.

A thorough explanation of some of the nuances of calculating and managing CVA, is presented by Damiano Brigo. It is far more than an introduction, and informs many of the posts which will take place here.