Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition

12.3 Impact of Default Probability and Recovery

We now consider the impact of default probability and recovery on CVA. There are several aspects to consider, such as the level of credit spreads, the overall shape of the credit curve, the impact of recovery rates and the basis risk arising from recovery rate assumptions. In all the examples below, we will consider the CVA of the same 5-year GBP payer interest rate swap, described in Section 12.2.2. The expected exposures are the same as those used previously in Chapter 9.¹³ The base case assumptions will be a flat credit curve of 500 bps and a recovery rate of 40%. The base case CVA is then calculated to be £91,389.

12.3.1 Credit Spread Impact

Let us first review the impact of increasing the credit spread of the counterparty in Table 12.1. The increase in credit spread clearly increases the CVA, but this effect is not linear since default probabilities are bounded by 100%. Another way to understand this is that the “jump to default” risk¹⁴ of this swap is zero, since it has a current value of zero and so an immediate default of the counterparty will not cause any loss. As the credit quality of the counterparty deteriorates, the CVA will obviously increase but at some point, when the counterparty is very close to default, the CVA will decrease again. This point will be discussed again in Chapter 16, as it is an important consideration for hedging.

Table 12.1 CVA of the base case IRS as a function of the credit spread of the counterparty. ...